Mr.DeMeo - HOMEWORK - Probabilities of draws without replacement calculator

Unit 10

Statistics & Probability

Grade 7ACC

Name:______________________

Teacher:____________________

Period:______________________

Lesson 1 – Statistical Questions Classwork Day 1

Vocabulary

Statistical - ____________________________________________________________________________

Variability - ____________________________________________________________________________

What is a statistical question? A statistical question is where you might expect many different answers.

Think(

Samantha wants to collect statistical information about the different sports seventh graders at her school like to watch.

She writes 3 questions to ask 50 seventh graders and will use the results to make an estimate about all seventh graders. Which questions are statistical and which are not?

When is the next home basketball game? Statistical or Not Statistical

What is your favorite sport to watch? Statistical or Not Statistical

What was the last sports game you watched at this school? Statistical or Not Statistical

When creating a statistical question we need to ask ourselves…

What are the possible answers to this question? Are the answers too general? Too Specific?

Explain in your own words the difference between a question that is statistical and one that is not.

____________________________________________________________________________________

___________________________________________________________________________________

___________________________________________________________________________________

Conclude: If there is any variability (more than one answer) then it is statistical. If the answer is a fact (only one answer) then it is non-statistical.

Try These

Determine whether each question is statistical or non-statistical. Then, explain your answer.

1. A political group asked voters waiting in line to vote: Who are the 2 major candidates running for president this year?_____________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

2. The journalism club surveyed students in the library and asked: About how much time do you spend reading each day?_____________________________________________________________________________

______________________________________________________________________________________

______________________________________________________________________________________

_____________________________________________________________________________________

3. To decide if a new movie should be shown this Friday, a movie theatre invited 50 people to view the movie and answer the question: Did you enjoy the movie? ___________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

Lesson 1 – Statistical Questions Classwork Day 1

1. Write both a statistical and a non-statistical question you could ask some classmates to make a prediction about teenagers and text messaging. ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. Which of the following questions has more variability?

A Did you play in the football game?

B What flavors of frozen yogurt does the yo-go mania offer?

Explain your answer ________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

Talk through these problems as a class. Then write your answers below.

3. Compare. Which question is statistical and which is not? Explain how you know.

• What is your favorite Olympic sport to watch?

• When are the next Olympic games?

____________________________________________________________________________________________________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

4. Analyze. Which is a better statistical question to ask your classmates if you are interested in finding out movies seventh graders enjoy watching? Explain

• What is the most recent movie you saw?

• What are three of your favorite movies?

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

5. Predict. Which statistical question would result in more variability? Explain.

• Do you own a scooter and/or bicycle?

• About how many hours per week do seventh graders participate in sports?

__________________________________________________________________________________________

__________________________________________________________________________________________

__________________________________________________________________________________________

Statistical Questions Homework Day 1

For 1 through 4, tell whether or not each question is statistical or non-statistical.

|1. What was the low temperature each day last month? |2. What color shirt am I wearing? |

| | |

| | |

|3. What size shoes do the students in your class wear? |4. How long does it take students in a class to read a book? |

| | |

| | |

For 5 through 8, write a statistical question that could be used to gather data on each topic.

|5. Distances members of the track team jogged last week |6. Numbers of letters in name of street |

| |you live on |

| | |

|7. Cost of a restaurant dinner |8. Numbers of cars of different colors in |

| |a parking lot |

| | |

9. The data shown are the responses to the question. How tall, in centimeters, is each bean plant? Make a dot plot to display the data.

8 6 7 5 8 6 8 7 9 4

5 2 8 6 9 5 7 6 7 7

10. What statistical question might Brittany have asked to get this data?

18 min, 20 min, 30 min, 16 min, 45 min

A How long did you spend on homework last night?

B How long do the directions say to cook the pie?

C At what time does school end?

D How many minutes does it take Eric to get to school?

11. Writing to Explain Wyatt says that statistical questions must involve numbers in the question. Do you agree with Wyatt? Explain.

Lesson 2- Sampling Classwork Day 2 Important Vocabulary:

Bias__________________________________________________________________________

Unbias___________________________________________________________________________________

Population: A whole group of people or objects Sample: A part of the group or population

Example: Example:

Sampling Methods:

Random Sample-___________________________________________________________________________

Systematic Sample-_________________________________________________________________________

Stratified Sample-__________________________________________________________________________

For each of the following, state which sampling method is being used:

1. 100 florists, chosen at random, are asked what their busiest season was: ____________________

2. 25 football players and 25 soccer players were asked which brand of sneaker they like: _____________

3. Every 10th customer at an auto shop was asked to evaluate the service: __________________________

4. 75 computer salespeople were asked, at random, which type of computer they sold most:_____________

5. 50 cat owners and 50 dog owners were asked what they liked most about owning a pet:_____________

6. Workers on an assembly line check every 10th tire: ___________________________

7. Names are drawn from a hat and selected to participate in a survey: _________________________

8. Students are surveyed in groups determined by grade level:_________________

9. Every tenth student from a list is selected to complete a survey:_________________

Biased Samples/Surveys:

Samples can be biased if they:

- Do not represent the entire population being surveyed -Are chosen based on convenience.

Ex: Ex:

-Involve only people who volunteer or want to be in the survey - A survey can also be biased if the questions

asked are leading questions.

Ex: Ex:

PASTA A grocery store asked every 20th person entering the store what kind of pasta they

preferred. The results are shown in the table. If the store decides to restock their shelves

with 450 boxes of pasta, how many boxes of lasagna should they order?

|Grade |Sample |Percent |

|6th |20 Students |20% |

|7th |20 Athletes |60% |

|8th |20 Students |20% |

Lesson 2 - Sampling Classwork Day 2 Example: A survey is conducted to compare the exercise habits of students in Seneca. The results are noted in the chart below:

[a] Is this survey biased? If so, why?

[b] How could this survey be more accurate?

Determine whether each of the following is BIASED or UNBIASED and explain:

1. A survey of teenagers that includes only teenage girls?

2. The survey question is: “Math is extremely important, what is the most important subject?”

3. A survey about favorite toys of 3 year olds that includes only 4 year olds

4. The survey question is: “What is your favorite movie?”

5. The survey question is: “People who don’t like The Hunger Games aren’t smart, what is your favorite movie?”

6. Questioning every 8th person who enters the cafeteria to see if they like school lunch.

Consider this survey. Mr. Coffey wants to know how the students in his school feel about a new dress code. He surveys all the students in his homeroom. Is his survey biased? If it is, what could he have done differently to make it representative?

Lesson 2 - Sampling Homework Day 2 (2 pages)

Match each of the following:

1. Population ______ A. Sampling method in which every individual or object in a population has an equal chance of being selected.

2. Random Sample ______ B. Sampling method in which a population is divided into subgroups that contain similar individuals or objects.

3. Sample ______ C. Whole group of people or objects.

4. Stratified Sample ______ D. Sampling method in which you select an individual and then follow a pattern to select the others.

5. Systematic Sample ______ E. Part of a group.

Determine the Type of Sample:

6. Every fifth person who leaves a hospital is asked how the health care was. ____________________

7. 20 men and 20 women were asked what their favorite spot was to vacation. ___________________

8. From a list of 300 teachers who attend a conference, 50 teachers are chosen. ___________________

9. 40 names were drawn out of a hat, without looking, and asked to take a survey._________________

10. A sample is grouped by grade-level._______________

Determine whether each is BIASED or UNBIASED, explain:

11. “Do you agree with the basketball coach that basketball is the best sport?”

12. A survey about what 7th graders eat for lunch includes boys.

13. A survey about what 7th graders eat for lunch only includes boys.

14. “What book did you enjoy reading the most this year?”

15. A survey is conducted, but only the closest four people were surveyed.

16. A survey about favorite movies is conducted in a movie store.

17. A survey about favorite hobbies is conducted in a sports store.

18. A bookstore surveys every fifth customer about customer service.

Continue to next page…

Lesson 2 - Sampling Homework Day 2

19. A school store sells binders in four different colors. A survey is conducted by the staff of the store to find the most popular color. The chart shows the results.

|Color |Number |

|Red |25 |

|Green |10 |

|Blue |13 |

|Yellow |2 |

a. If a student from the survey is chosen at random, what is the probability that this student chose red?

b. What percentage of the sample chose blue?

c. What percentage of the sample chose red?

d. If 450 binders are to be ordered to stock the school store, how many should be green?

e. Determine whether each of the following samples is biased or unbiased:

[1] Only boys are included.

[2] Every tenth student that walks into the school is surveyed.

[3] Students are selected at random through the use of a computer algorithm.

[4] Students are asked to volunteer to take the survey.

[5] Only Mr. Oakes’s first class was surveyed.

[6] Twenty-five girls and twenty-five boys were surveyed.

20. Suppose you want to find out the times of day teenagers listen to the radio. Determine whether each of these samples is biased or unbiased:

a) Randomly surveying 100 listeners that are girls:_____________________

b) Randomly surveying 100 listeners that teenagers: _______________________

c) Surveying a group of boys and a group of girls, all of which are teenagers:_______________

d) Surveying only people listening to the radio at 4:00 in the afternoon:_____________

e) Surveying fifty 35 year old men and fifty 35 year old women:____________

f) Surveying only people who want to participate in the survey:____________

g) Randomly choosing 40 teenagers to participate:___________

Review

21. What is 5% of 600 22. What percent of 70 is 35?

23. An item costs $20 after a 20% discount was taken. What was the original price?

Lesson 3 – Measures of Central Tendency Classwork Day 3

Important Vocabulary:

Measures of Central Tendency: _______________________________________________________________

Mean: ____________________________________________________________________________________

Median:___________________________________________________________________________________

Mode: ____________________________________________________________________________________

Range: ___________________________________________________________________________________

Outlier: __________________________________________________________________________________

Given the following scores, what is the outlier or extreme value? 86, 82, 95, 32, 88

Inference______________________________________________________________

EXAMPLE: For the following set of data, find the mean, median, mode, and range. Make a dot plot to illustrate the given data.

2, 3, 5, 5 , 5, 6, 7, 9, 11, 11

MEAN MEDIAN MODE RANGE

1 2 3 4 5 6 7 8 9 10 11

Find the mean, median, mode, and range using the data from the stem and leaf.

Stem Leaf Write the data on the line ___________________________________________

7 2 9

8 0 5 5

9 7

|Measure of Central Tendency |Most Useful When… |

|MEAN | |

|MEDIAN | |

|MODE | |

[1] Which central tendency (mean, median or mode) would be best to use with the following data:

a) 90, 92, 88, 95, 30, 91 b) 3, 3, 6, 3, 4, 3, 3, 5 c) 95, 92, 93, 94, 90, 95

d) 30, 29, 31, 30, 30, 30 e) 91, 89, 92, 90, 88, 93 f) 80, 82, 85, 88, 61, 87

g) 120, 117, 119, 21, 122 h) 91, 91, 91, 90, 91, 97 i) 75, 77, 72, 73, 78, 79

Lesson 3 – Measures of Central Tendency Classwork Day 3

[2] Christopher would like to have an average of 96 in his math class. So far, he has scored a 98, 98, 94, and 100. What is the lowest grade Christopher can get to maintain a 96 average?

[3] Jill needs an average score of 92 on five quizzes to earn an ‘A’. The mean of her first four scores was 91. What is the lowest score that she can receive on the fifth quiz to earn an A (92)?

[4] Kieran had an average of 97 on his first 4 tests. After his fifth test, his average dropped to 95. What was his score on the fifth test?

[5] Nick scored a 91, 81, and 92 on three tests. What does Nick need on the fourth test to bring his average up to a 90?

[6] Susan has four 20-point projects for math class. Susan’s scores on the first 3 projects are shown below:

Project 1: 18

Project 2: 15

Project 3: 16

Project 4: ??

What does she need to make on Project 4 so that the average for the four projects is 17? Explain your reasoning.

Lesson 3 – Measures of Central Tendency Homework Day 3

Find the mean, median, mode, and range for each set of data. Round to the nearest tenth, if necessary.

1) Mike’s test scores: MEAN:_______ MEDIAN:________ MODE:________ RANGE:________

Stem Leaf

5 0 Write the scores on this line: _50, 74,_______________________________________

6

7 4 8

8 2 4

9 0 0

10 0

2) Inches of rain: 4, 6, 12, 5, 8

MEAN:_______

MEDIAN:________

MODE:________

RANGE:________

3) Annual inches of snow:

x

x x x x

x x x x x x x

[pic]

MEAN:______

MEDIAN:________

MODE:________

RANGE:________

4) Dominic would like to have an average of 85 in his math class. So far, he has scored a 78, 92, 80, and 82. What is the lowest grade Dominic can get to maintain a 85 average? (set up the equation)

Review

5) A pair of socks went from $5 to $6, what is the percentage change?

6) Simplify 2( 3x + 5) - [pic](6x + 18) 7) Subtract [pic] Go to Next Page

Lesson 3 – Measures of Central Tendency Homework Day 3

5) The ages of five children in a family are 3, 3, 5, 8, and 18. Which statement is true for this group of data?

a) median = mode b) median > mean

c) mean > median d) mode > mean

6) A shoe store owner is looking at a bar graph that shows the different styles of shoes he sold over the past 6 months. Which of the following measures would indicate the most popular style?

a) mode b) median

c) mean d) range

7) For five math tests, Danielle has an average of 88. What must she score on the 6th test to bring her average up to exactly 90?

a) 94 b) 100

c) 92 d) 98

8) Caitlyn learned to ride a unicycle. She practiced riding the unicycle for 25 minutes on Monday, 10 minutes on Tuesday, 22 minutes on Wednesday, 31 minutes on Thursday, and 13 minutes on Friday. What is the range for the data?

a) 5 minutes b) 12 minutes

c) 21 minutes d) 31 minutes

9) The temperature in Alaska was recorded every 4 hours over the course of a day. The results are shown below:

|Time |Temp |

|12:00 am |-12° |

|4:00 am |-2° |

|8:00 am |4° |

|12:00 pm |7° |

|4:00 pm |8° |

|8:00 pm |2° |

[a] What is the range of this data?

[b] What was the average temperature in Alaska for this day?

Lesson 4 - Mean Absolute Deviation MAD Classwork Day 4

Vocabulary

Outlier/Extreme Value - __________________________________________________________________

Mean - _________________________________________________________________________________

Absolute Value - _________________________________________________________________________

Deviate - ________________________________________________________________________________

Absolute Deviation = absolute value of the deviation

Mean Absolute Deviation (MAD) It tells you how the data is spread out compared to the mean.

Variability -

Mean (average) absolute deviation (MAD) is calculated by taking the mean of the absolute deviations for each data point. We do not use this method of describing data when there is an outlier or extreme value.

Vary – to differ

Ex) the houses vary in size

Measures of variation is similar to measures of central tendency (mean, median, and mode) because it helps us describe the data. Measures of central tendency help us describe the center of a set of data. Measures of variation show how close together the data in a set are or how far apart data points are.

How do you calculate mean absolute deviation?

Step 1 – calculate the mean of the data.

Step 2 – subtract the mean and each data point.

Step 3 – take the absolute value (distance is always positive)

How far away from the mean are you? Ex. Mean = 10 #12?______

Step 4 – Take the average of the absolute deviations.

Guided Practice Ex #1: Plant Heights: 18, 27, 21

Mean: 22

|Data |Mean |Calculate the Deviation |Absolute deviation |

|x |[pic] |[pic] | |

|18 |22 |[pic] |4 |

|27 | | | |

|21 | | | |

Mean Absolute Deviation =

Conclusion: The plant heights vary by an average of ________________inches from the mean.

Ex #2: Data: 5, 6, 7, 9, 10, 12, 20

Mean: 9.86 (rounded to the nearest hundredth)

|Data |Mean |Calculate the Deviation |Absolute deviation |

| |[pic] |[pic] | |

|5 |9.86 |[pic] |4.86 |

|6 |9.86 | |3.86 |

|7 |9.86 | | |

|9 |9.86 | | |

|10 |9.86 | | |

|12 |9.86 | | |

|20 |9.86 | | |

Find the mean absolute deviation. Round to the nearest tenth. Show work

Mean Absolute Deviation = 3.551428…… ( 24.86 divided by 7) answer: 3.6

Ex #3: Data: 10, 20, 30, 1000, 1500

Mean: 512

|Data |Mean |Calculate the Deviation |Absolute deviation |

| |[pic] |[pic] | |

|10 | | |502 |

|20 | | |492 |

|30 | | | |

|1000 | | | |

|1500 | | | |

Find the mean absolute deviation.

Mean Absolute Deviation = 590.4 (2952 divided by 5)

How do the two data sets compare in examples 2 and 3? Explain what you know and how you know it.

Multiple Choice Practice

4. The following data are given: 12, 9, 16, 23, 30, 9, 6, 15, 18, and 23. Which of the following shows the mean and MAD for these data?

A. Mean = 16.1, and MAD = 16.1 B. Mean = 16.1, and MAD = 5.92

C. Mean = 5.92, and MAD = 5.92 D. Mean = 5.92 and MAD = 16.1

| |Mean |MAD |

|Team A |18.6 |4 |

|Team B |12 |1 |

5. Look at the table to the right.

Which statement CANNOT be made about these data?

A On a dot plot, Team A will be farther to the right, and the dots will be spread out.

B On a dot plot, Team B will be farther to the left, and the dots will be clustered.

C The mean for Team A was determined from more scores than the mean for Team B.

D Not Here

Lesson 4 - Mean Absolute Deviation MAD Homework Day 4

1. Rachel and Molly are in the same reading class. Rachel’s scores on her first three vocabulary quizzes were 79, 86, and 90. Molly’s scores were 70, 78, and 80. Calculate the means and the mean absolute deviations of their quiz scores. Compare them.

step 1: Calculate the MAD for Rachel’s scores Step 2: Calculate the MAD for Molly’s scores

|Data point, |mean |absolute deviation |Absolute |

|x | |from mean |deviation |

| | |[pic] | |

| | | | |

| | | | |

| | | | |

Whose scores deviated more from the mean? Rachel or Molly Explain________________________

____________________________________________________________________________________

Review

2) Below is the data collected from two random samples of 100 students regarding student’s school lunch preference.

|Student Sample |Hamburgers |Tacos |Pizza |Total |

|#1 |12 |14 |74 |100 |

|#2 |12 |11 |77 |100 |

Make at least two inferences based on the results.

1.

2.

3) The school food service wants to increase the number of students who eat hot lunch in the cafeteria. The student council has been asked to conduct a survey of the student body to determine the students’ preferences for hot lunch. They have determined two ways to do the survey. The two methods are listed below. Determine if each survey option would produce a random sample. Which survey option should the student council use and why?

1. Write all of the students’ names on cards and pull them out in a draw to determine who will complete

the survey.

2. Survey the first 20 students that enter the lunchroom.

3. Survey every 3rd student who gets off a bus.

Next Page

Lesson 4 - Mean Absolute Deviation MAD Homework Day 4

Jason wanted to compare the mean height of the players on his favorite basketball and soccer teams. He thinks the mean height of the players on the basketball team will be greater but doesn’t know how much greater. He also wonders if the variability of heights of the athletes is related to the sport they play. He thinks that there will be a greater variability in the heights of soccer players as compared to basketball players. He used the rosters and player statistics from the team websites to generate the following lists. Was he correct? Explain

Basketball Team – Height of Players in inches for 2010 Season

75, 73, 76, 78, 79, 78, 79, 81, 80, 82, 81, 84, 82, 84, 80, 84

Soccer Team – Height of Players in inches for 2010

73, 73, 73, 72, 69, 76, 72, 73, 74, 70, 65, 71, 74, 76, 70, 72, 71, 74, 71, 74, 73, 67, 70, 72, 69, 78, 73, 76, 69

To compare the data sets, Jason creates a two dot plots on the same scale. The shortest player is 65 inches and the tallest players are 84 inches.

Lesson 5 – Variability – Box plot Classwork Day 5

Important Vocabulary:

Variability:________________________________________________________________________________

Remember the more choices (answers to a question) or the more numbers are spread out from the mean, the more variability.

Box Plot:________________________________________________________________________________

________________________________________________________________________________________

Interquartile Range (IQR)___________________________________________________________________

__________________________________________________________________________________________

Mean Absolute Deviation (MAD)____________________________________________________________

Remember: Median is paired with the interquartile range and mean is paired with the mean absolute deviation .

Guided Instruction - Box-Plots: Use the shown box-plot to answer the questions:

What is the least value?

What is the lower quartile?

What is the median?

What is the upper quartile?

What is the greatest value?

What is the range?

What is the interquartile range (IQR)?

Practice:

1. What is the least value?

2. What is the upper quartile?

3. What is the median?

4. What is the range?

5. What is the greatest value?

6. What is the lower quartile?

7. What is the interquartile range?

Lesson 5 – Variability – Box plot Classwork Day 5

8. Construct a box plot to represent the following data. Be sure to label the minimum, maximum, median, upper quartile, and lower quartile. 12, 11, 9, 18, 10, 11, 7, 16, 14, 11, 6

Step 1: Order the #’s from least to greatest on the line below:

_______________________________________________________

Step 2: Find the median of the numbers listed in step 1 and circle/list it. Next, put brackets around the numbers to the right and numbers to the left.

Step 3: Find the median of scores to the left and right of the median. (circle them)

Step 4: List all the important information to display the data on a box and whiskers.

Minimum ________

Maximum________

Median __________

Lower Quartile ________

Upper Quartile ________

a. What is the least value? b. What is the lower quartile? c. What is the median?

d. What is the upper quartile? e. What is the greatest value? f. What is the range?

g. What is the interquartile range?

Patrons in the children’s section of a local branch library were randomly selected and asked their ages. The librarian wants to use the data to infer the ages of all patrons of the children’s section so he can select age appropriate activities. In questions 11-13, complete each inference.

7, 4, 7, 5, 4, 10, 11, 6, 7, 4

9. Make a box plot (box and whiskers) of the sample population data

Minimum ________

Maximum________

Median __________

Lower Quartile ________

Upper Quartile ________

10. Make a dot plot of the sample population data.

11. The most common ages of children that use the library are ______ and ______.

12. The range of ages of children that use the library is from ______ to ______.

13. The median age of children that use the library is ________.

Lesson 5 – Variability Homework Day 5

1. What is the least value? 2. What is the lower quartile?

3. What is the median? 4. What is the upper quartile?

5. What is the greatest value? 6. What is the range? 7. What is the interquartile range?

8. Construct a box plot for the following scores: 3, 5, 9, 8, 4, 7

Minimum ________

Maximum________

Median __________

Lower Quartile ________

Upper Quartile ________

9. Find the MAD of each dot plot. Create a table to show work.

Race Times (min)

10. Finding the Mean Absolute Deviation (MAD): Inches of Rain in the Last Eleven Days

Remember the steps: Draw a table to help you.

Step 1: Find the mean of the data

Step 2: Find the absolute value of the differences

between each value and the mean.

Step 3: Find the average of the mean deviations.(MAD)

Make a table to help you.

Lesson 6– Variability mixed practice Classwork Day 6

Vocabulary

Symmetrical _________________________________________________________________

Draw a line(s) of symmetry for the following figures.

Symmetry of Box-Plots: Which is symmetrical? Write the percent on the line.

A B

Which plot has more variability, A or B? ______ Explain _______________________________________

______________________________________________________________________________________

Looking at set A what percent of data is at least 2? ________________________

Comparing Two Populations:

Examples:

Samantha surveyed a different group of students in her science and math classes. The double box plot shows the results for both classes. Compare their centers and variations. Write 4 inferences you can draw about the two populations.

Number of TV shows watched this week

Is there overlap? yes or no If so, please describe the overlap?

Lesson 6– Variability mixed practice Classwork Day 6

1. The double box plot shows the costs of MP3 players at two different stores. Compare the centers and variations of the two populations. Write at least 3 inferences you can draw about the two populations.

Cost of MP3 Players

Is there overlap? yes or no If so, describe the overlap.

2. The double dot plot below shows the daily high temperatures for two cities for thirteen days. Compare the centers and variations of the two populations. Write 2 inferences you can draw about the two populations.

Daily High Temperatures

Inference 1__________________________________________________________________________

Inference 2 __________________________________________________________________________

Lesson 6– Variability mixed practice Homework Day 6

1. The double box plot shows the daily participants for two zip line companies for one month. Compare the centers and variations of the two populations. Which company has the greatest number of daily participants?

Number of Daily Participants

a) Which zip line company has more variability? Explain ______________________________________

_______________________________________________________________________________________

b) Is there overlap? yes or no If so describe the overlap.

c) Make at least 2 inferences based on the box plots.

Inference #1 ____________________________________________________________________________________

Inference #2 ____________________________________________________________________________________

Inference #3 ____________________________________________________________________________________

2. The double dot plot shows the number of new emails in each of Mike’s and Hannah’s inboxes for 16 days.

Number of Emails in Inbox - Mike

Number of Emails in Inbox - hannah

Compare the centers and variations of the two populations. Write an inference you can draw about the two populations. ____________________________________________________________________________________________________________________________________________________________________________________

Do these two sets overlap? NEXT PAGE

Lesson 6– Variability mixed practice Homework Day 6

The dot plots compare the number of raffle tickets sold by boys and girls during

a school fundraiser.

1. Which plot has an outlier?

A Girls B Boys C both plots D neither plot

2. What is the difference between the medians for the two data sets?

A 0 tickets B 2 tickets C 4 tickets D 6 tickets

Use the box plots for 3 and 4.

3. What is the interquartile range for the Checkers Club?

A 4 B 5 C 10 D 11

4. Which data set shows a greater spread?

A Chess Club B Checkers Club C They have the same spread. D You cannot tell from the box plots.

Use the dot plots for 5–7.

The dot plots show the number of hours students in two classes studied.

5. What percent of each class studied less than 4 hours? 6. Find the medians.

Math: ____________ Science: __________ Math: ____________ Science: __________

7. Compare the centers and spreads.

Histograms Classwork Day 7

Vocabulary

Intervals - __________________________________________________________________________

Frequency - _________________________________________________________________________

Cumulative Frequency - _______________________________________________________________

Data from a frequency table can be displayed as a histogram. A histogram is a type of bar graph used to display numerical data that have been organized into equal intervals.

Answer the following question using the histograms below:

Histograms Classwork/Homework Day 7

7) Construct a cumulative frequency table for the age of students who read Garfield:

8, 12, 16, 20, 22, 15, 7, 8, 11, 13, 14, 9, 14, 8, 10, 21, 18, 11, 13, 9

|Age Group in intervals |Tally |Frequency |Cumulative Frequency |

|5-9 | | | |

| | | | |

|10-14 | | | |

| | | | |

|15-19 | | | |

| | | | |

|20-24 | | | |

8) Construct a cumulative frequency table for the age of students in a college night course:

26, 36, 34, 39, 38, 31, 21, 23, 20, 22, 24, 31 29, 24, 29, 39, 28, 39, 32, 35

Use the Intervals of 20-24, 25-29, 30-34, 35-39

|Age Group in intervals |Tally |Frequency |Cumulative Frequency |

| | | | |

|20-24 | | | |

| | | | |

| | | | |

| | | | |

Construct a histogram using the frequency.

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

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| | | | |

Study Guide - HOMEWORK HELP!!!!!

The double dot plot shows the height in inches for the girls and boys in Franklin’s math class. Compare the centers and variations of the two populations. Round to the nearest tenth. Write an inference you can draw about the two populations.

Girls

Remember…

Both Symmetrical Mean and MAD (Mean Absolute Deviation)

[pic]

Outcomes Classwork Day 8

Important Vocabulary:

Outcomes:________________________________________________________________________________

Sample Space: _____________________________________________________________________________

Fundamental Counting Principle:_______________________________________________________________

Example: Complete the tree diagram for tossing a coin three times.

a) P(HHH) = b) P(TTT) =

c) P(at least one H) = d) P(exactly 2 T’s) =

e) If you tossed 4 coins, how many possible outcomes would there be?

Tree Diagrams: Displays all outcomes in detail

Make a tree diagram to represent the sample space of flipping a balanced coin and rolling a fair die.

Total Outcomes:_______

What is the probability of the coin landing on tails and rolling an even number?

A pizza shop offers the following options for a slice of pizza: 1. TYPE: Regular or Sicilian

2. CRUST: Thin or Thick 3. TOPPINGS: Pepperoni, Sausage, Meatball, or Anchovies

Make a tree diagram to represent the sample space of the various slices that could be made.

Outcomes Classwork Day 8

Fundamental Counting Principle (FCP): Allows us to determine the number of outcomes in a sample space by multiplying the number of ways each event can occur.

Examples:

A pizza shop offers the following options for a slice of pizza:

TYPE: Regular or Sicilian

CRUST: Thin or Thick

TOPPINGS: Pepperoni, Sausage, Meatball, or Anchovies

Use the FCP to determine the total number of possible slices of pizza.

1. A restaurant has four different appetizers, three different entrees, and two different desserts on their price-fixed menu. How many different outcomes can there possibly be?

2. If Mr. DeMeo has fifteen pairs of pants, twenty-three collared-shirts, and sixty-four ties; what are the total number of outfits that he can possibly create?

3. If a student rolls two dice, what is the number of total outcomes?

4. Find the total number of different outfits that can be made from the following:

3 different sweaters, 4 turtlenecks, and 2 pairs of jeans.

5. When rolling a fair die and flipping a balanced coin, what is the total possible outcomes?

Outcomes Homework Day 8

1. Create a tree diagram and list the sample space representing all possible outcomes of flipping a coin twice.

2. Create a tree diagram and list the sample space representing all possible outcomes of rolling a fair die twice.

3. Create a tree diagram and list the sample space representing all possible outcomes of choosing a hat that comes in black, red, or white AND medium or large.

4. Create a tree diagram and list the sample space representing all possible outcomes of choosing peach or vanilla yogurt topped with peanuts, chocolate, strawberries, or granola.

5. At a wedding you can choose from 4 different meats (lobster, steak, chicken, or pork). You can choose from 2 side dishes (pasta or vegetables) and from 2 desserts (fruit or ice cream). How many total outcomes are possible? Use the FCP.

6. At dinner you have the choice of 3 different soups, 4 appetizers, 5 main meals, and 3 desserts. Find the number of possible outcomes of choosing 1 of each course from the menu.

Simple Events/Theoretical Classwork Day 9

Important Vocabulary:

Probability: The chance that some event will happen; the ratio of ways a specific event can happen to the total number of outcomes.

[pic]

*Probability can be expressed as a fraction, a decimal, or a percentage.*

Complementary Events: the set of all outcomes in the sample space that are not included in the event. Example: Rolling a 3 on a number cube is 1/6 the complement is 5/6 ( numbers 1, 2, 4, 5, 6)

P(event) + P(complement) = 1

Examples:

1. A fair coin is flipped, what is the probability of getting a ‘tails’?

Percent___________ Fraction___________ Decimal__________

2. The probability that it rains today is 60%. What is the probability that it does not rain?

Percent___________ Fraction___________ Decimal__________

3. A spinner consists of six equal sections numbered 1-6.

What is the probability of the spinner landing on 5?

a) Find P(3). b) What is the probability of getting an even number?

c) What is P(3 or 4)? d) What is the probability of the spinner landing on 7?

4. John has eight red marbles and four blue marbles in a jar. What is the probability that John picks a marble at

random, and it is not red?

Answer the following questions to demonstrate knowledge of probability:

5. What is the sum of the probabilities of all the outcomes in a sample space?

6. The probability of a certain event occurring is [pic] .

Express this probability as a decimal. Express this probability as a percentage.

What is the probability that this event does not occur?

Simple Events/Theoretical Classwork Day 9

7. Which of these cannot be considered a probability of an outcome? Explain.

[a] [pic] [b] -0.59 [c] 1 [d] [pic] [e] 0

[f] [pic] [g] 0.80 [h] 1.45 [i] 112% [j] 100%

[pic] [pic] [pic]

Describe each event as impossible, likely, unlikely, or certain.

8. The probability of tossing a number cube and getting 5 is [pic]. _________________

9. The probability of spinning blue on a spinner is 0. ___________________________

10. The probability of selecting a red marble from a bag of marbles is 0.47. ____________________

11. The probability of selecting a tile with a vowel on it from a box of tiles is [pic]. ________________

12. If a fair die is rolled one time, find the probability of the following outcomes:

[a] rolling a four

[b] rolling an even number

[c] rolling a number greater than four

[d] rolling a number less than seven

Which was most likely to occur (a, b, c or d)?

13. A box contains 5 green pens, 3 blue pens, 8 black pens, and 4 red pens. One pen is picked at random.

[a] What is the probability the pen is green?

[b] What is the probability the pen is blue or red?

[c] What is the probability the pen is gold?

14. The spinner is used for a game. Write each probability as a fraction.

[a] P(3) [b] P(5) [c] P(1 or 2) [d] P(odd) [e] P(a number at most 2)

Simple Events Classwork Day 9

15. A spinner has eight congruent sections, which are colored in the following way:

[i] 2 Red Sections

[ii] 2 Yellow Sections

[iii] 1 Blue Section

[iv] 3 Green Sections

What is the probability of the following outcomes:

[a] Spinning a Red

[b] Spinning a Red or a Green

[c] Spinning a Yellow or a Blue

[d] Not Spinning a Color in the American Flag

[e] Spinning a Purple

Deck of Playing Cards

I. 52 total cards (four suits of each - ♥ ♦ ♣ ♠)

a. Face Cards (Jack, Queen, King)

b. Other cards (2-10, and Ace)

18. If a magician asks you to select one card from a fair deck of cards, find:

[a] P(ace) [b] P(red) [c] P(not a diamond) [d] P(Queen of spades)

[e] Probability of selecting a Spade or a Diamond [f]Probability of selecting a red picture card

[g] Probability of selecting a 1

19. A weather forecast states that there is an 80% probability of rain tomorrow. Which term best describes the likelihood of rain tomorrow?

A. Impossible B. Unlikely C. Likely D. Certain

Simple Events Homework Day 9

1. A spinner with six equal sections is used for a game. The sections are numbered 1-6 Write each probability as a fraction.

P(3) b. P(7) c. P(3 or 4) d. P(even) e. P(not 5)

2. A bag contains 4 red marbles, 3 orange marbles, 7 green marbles, and 6 blue marbles. Express each probability as a fraction:

P(red) b. P(green) c. P(red or blue) d. P(not green) e. P(purple)

3. If the probability that it will snow tomorrow is 0.85, what is the probability that it will not snow tomorrow?

4. There is a 30% chance that it will rain on Saturday. What is the probability that it will not rain?

#’s 5 – 6 Describe each event as impossible, likely, unlikely, or certain.

5. The probability of a spinner landing on a shaded section is 53%.

6. The probability of tossing a number cube and rolling a number greater than 1 is [pic].

7. A company that manufactures light bulbs finds that one out of every twenty light bulbs are defective.

a) Express, as a fraction, the probability that a random light bulb is defective. (defective-broken)

b) Express, as a fraction, the probability that a random light bulb is not defective.

c) In a sample of 100 light bulbs, how many bulbs should the company expect to be defective?

d) The manager of your branch of the company tells you that 20% of the light bulbs manufactured are

defective. Is this an accurate statement?

16. There are 4 aces and 4 kings in a standard deck of 52 cards. You pick one card at random. What is the probability of selecting an ace or a king? Explain your reasoning.

______________________________________________________________________________________________

______________________________________________________________________________________________

17. Reasoning: A box contains 150 black pens and 50 red pens. Chris said the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1. Explain whether you agree. ______________________________________________________________________________________________

______________________________________________________________________________________________

______________________________________________________________________________________________

Mixed Review

8. Simplify: 3(2x – 3) – 10(x – 2) 9. -2x and 2x are additive inverses because….

10. Solve: 3x – 5x = 4 11. Solve: 3x > -9 12. Solve: -3x > -9

Independent Events Classwork Day 10

Important Vocabulary:

Compound Event: _________________________________________________________________________

Independent Event: ________________________________________________________________________

Dependent Event: _________________________________________________________________________

Determine if each of the following events are considered independent or dependent:

[a] Tossing a coin and drawing a card from a deck.

[b] Drawing a marble from a jar, not replacing it, and then drawing a second marble.

[c] Driving on ice and having an accident.

[d] Having a large shoe size and having a high IQ

[e] Not studying for a test and receiving a low test score.

[f] Picking a card from a deck, replacing it, and choosing another card.

[g] Picking a card from a deck, and then choosing another card without replacing the first.

[h] Picking a marble from a jar, replacing it and picking another marble.

[i] Committing a crime and getting arrested.

[j] Not eating dinner and being hungry at 8:00 pm.

[k] The Giants winning the Super Bowl and the Rangers winning the Stanley Cup.

To find the probability of compound independent events, multiply the probability of each event.

[pic]

Examples 1:

When flipping a coin twice, what is the probability of getting two tails?

Example 2: A game calls for the player to flip a coin and then roll a fair die. Find each probability:

[a] P(tails and 4) [b] P(heads and odd) [c] P(tails and 7)

Independent Events Classwork Day 10

Practice:

1. A person draws a card from a deck of cards, puts the card back and picks again. Find the following probabilities:

[a] P(red and red) [b] P(5 of clubs and 7 of spades)

[c] P(two face cards) [d] P(two spades)

2. There are 4 green marbles, 5 red marbles, 9 blue marbles, and 2 orange marbles in a jar. One marble is selected at random, replaced, and another is selected. Find the following probabilities.

[a] P(green and blue) [b] P(red and orange) [c] P(red and yellow)

[d] P(two blue marbles) [e] P(no red marbles) [f] P(red or blue, and green)

3) An arrangement of 8 students is shown. The numbers of all the students are in a basket. The teacher selects a number and replaces it. Then the teacher selects a second number. Find each probability.

|Row |Student |

|A |1 |2 |3 |4 |

|B |5 |6 |7 |8 |

a) P(student 1, then student 8) =

b) P(student in row A, then student in row B) =

c) P(student in row A, then student 6, 7, or 8) =

Independent Events Homework Day 10

1. A spinner has eight equal sections numbered 1-8. The spinner is spun twice. Find the following probabilities:

[a] P(1 and 2) [b] P(3 and 3) [c] P(odd and even) [d] P(1 and not 1)

[e] P(7 and 0) [f] P(1 and 0) [g] P(not 0 and not 7) [e] P(both numbers < 4)

2. A company produces two different sized light bulbs. One out of every 25 big bulbs is defective. One out of every 50 small bulbs is defective.

a) What is the probability that when purchasing one of each, both will be defective?

b) What is the probability that when purchasing only one small bulb, the bulb will not be defective?

c) In a sample of 200 big bulbs, how many defective bulbs are to be expected?

d) In a sample of 200 small bulbs, how many defective bulbs are to be expected?

3. What is the probability of flipping a coin 3 times and getting heads every time?

4. What is the probability of getting five consecutive tails when flipping a coin five times?

5. A spinner has four equal sections numbered 1 though 4. You spin it twice. Use the sample space below to find each probability. Second Spin

a) P(1,2) b) P(1,odd) c) P(even, odd)

Dependent Events Classwork Day 11

To find the probability of compound dependent events, multiply the probability of the first event and the probability of the second event after the first event happens. (Remember- “Probability Land”- you get to pick one at a time but you get what you want()

[pic]

Describe in your own words the phrase “without replacement”.

____________________________________________________________________________________

Example:

There are 4 green marbles, 5 red marbles, 9 blue marbles, and 2 orange marbles in a jar. One marble is selected at random, and then another is selected without replacement.

a) Find the probability that two blue marbles will be selected

Step 1 : Find the probability of the first event happening:

P(first marble is blue) =

Step 2: Find the probability of the second event happening, assuming the first event did happen:

P(second marble is blue) =

Step 3: Multiply the probabilities of each event:

P(two blue marbles) =

b) Find the probability that the first marble will be red and the second will be green:

P(Red and then Green) =

1. A mason jar contains eighteen marbles in the following colors:

[i] 6 green marbles

[ii] 4 blue marbles

[iii] 7 red marbles

[iv] 1 black marble

What is the probability of the following outcomes without replacement?

[a] P(green and then blue) [b] P(two reds) [c] P(black and then black)

[d] P(two blacks) [e] P(red and then green) [f] P(black and then not black)

[g] P(green and then not red) [h] P(two blues)

Dependent Events Classwork Day 11

2. Five girls and seven boys want to be the two broadcasters for a school show. To be fair, a teacher puts their names in a hat and selects two. Find P(girl, then boy).

Make a Plan: The selections of the two names are (dependent or independent) events? Find the probability of selecting girl first. Then find the probability of selecting a boy after selecting a girl.

Carry out the Plan: P(girl first) = P(boy after girl) =

Final answer: P (girl, then boy) =

3. A student writes the numbers (1-9) on index cards, and then places them in a hat. If another student draws two cards without replacing them, what is the probability of:

[a] P(8 and then 5) [b] P(both digits being even)

[c] P(both digits being odd) [d] P(both digits being perfect squares)

[e] P(1 and then 2) [f] P(9 and then a number less than 9)

[g] P(both numbers greater than 5) [h] P(both numbers are prime)

Easy Medium Challenging

|4. |5. A box contains 20 cards numbered 1-20. You |6. The face cards are removed from a standard deck |

| |select a card. Without replacing the first card, you |of 52 cards, and the rest are set aside. Two cards |

| |select a second card. Find each probability. |are drawn at random from the face cards. Once a card |

| | |is selected, it is not replaced. Find each |

|You select the letter A from the group. Without |a) P(1, then 20) = |probability. |

|replacing the A, you select a second letter. Find | |a) P(2 queens) = |

|each probability. |b) P(3, then even) = | |

|a) P(Z) = | |b) (black jack and then red queen) = |

|b) P(grey) = |c) P(even, then 7) = | |

|c) P(consonant) = | |c) P(black jack and then black card) = |

|d) P(vowel) = | | |

Dependent Events Homework Day 11

1. Mr. DeMeo has to select two students from class to join the SLAM. He decides to choose randomly from a class of eleven girls and nine boys.

[a] What is the probability that he will choose a girl first and then a boy second?

[b] What is the probability he will choose a boy first and then a girl second?

2. There were 5 cards in a bag labeled 0 through 4. Find each probability if two cards are picked with no replacement. (Write the numbers down to help you()

[a] P(2 and then 4) [b] P(2 and then 2) [c] P(1 and then 2 and then 3)

[d] P(prime # and then 0) [e] P(three 0’s) [f] P(# less than 2 and then a 4)

3. In a standard deck of cards:

[a] What is the probability of picking a king or a queen?

[b] What is the probability of picking a king and then a queen with replacement?

[c] What is the probability of picking a king and then a queen without replacement?

[d] What is the probability of picking four consecutive aces without replacement?

Review

4. In a board game, you randomly select one number card and one category card. The possible numbers are 1,2 and 3. The possible categories are Science, History, Sports, Language, and Math. Assume that each outcome is equally likely. Make a tree diagram and sample space to display the outcomes. (Separate Paper please-This may be collected()

5. William can spend no more than $15 at a carnival. The entrance fee to the carnival is $7, and rides cost $2 each. Which inequality best represents the number of rides r that William can afford?

a) r ≤ 4 b) r < 4 c) r ≤ 11 d) r < 11

Experimental Probability Classwork Day 12

Important Vocabulary:

Theoretical Probability:____________________________________________________________________

Empirical (Experimental) Probability:_____________________________________________________________

THEORETICAL EXAMPLE: What should happen(.

1. A fair coin is flipped four times.

[a] What is the probability that the first flip will be heads?

[b] What is the probability that all four flips will be tails?

[c] How many times would you expect to get tails in the four flips?

[d] If you were to flip the coin a total of 100 times, how many times would you expect heads to appear?

EMPIRICAL(EXPERIMENTAL)EX.: BASED ON OBSERVED DATA-What actually did happen(.

2. A probability experiment is conducted. In the experiment, a BALANCED coin is flipped 20 times. The results are displayed in the graph below:

| |1 |2 |

|Tails | | |

| | | |

Use your data to find the experimental probability of:

a) P (heads) b) P(tails) c) P(heads or tails)

3. Write a conclusion comparing the results from your experiment and the theoretical probability.

4. How many heads would you expect when flipping a fair balanced coin fifty times?

5. How many primes would you expect when rolling a fair die one hundred times?

6. How many times would you expect to pick a diamond, if you selected a card from a fair deck thirty-two times?

7. How many times would you expect to roll a 5 when rolling a fair die twelve times?

Experimental Probability homework Day 12

8. The odds of a particular team to win the Super Bowl are 1/8. If these odds stayed consistent every year, how many super bowl titles would you expect this team to have in the next 80 years?

9. A fair die is rolled twice.

How many possible outcomes are there?

What is the probability of rolling a 3 and then a 5?

10. A company that produces car parts tests a sample of fifty parts. After testing all fifty parts, they find that 7 parts are defective.

[a] What is the experimental probability of a part being defective?

[b] What is the experimental probability of a part being functional?

[c] How many defective parts would you expect in a batch of 1000 parts?

[d] How could the company find a more accurate representation of their defective parts?

11. A particular game of chance is played by flipping a coin, rolling a fair die, and then picking a card from a fair deck. What is the probability of winning the game if:

[a] Winning means (heads, one, ace)

[b] Winning means (tails, odd, black)

[c] Winning means (heads, prime, picture card)

12. Which of the following shows a proportional relationship?

|Y |13 |12 |9 |

|X |5 |4 |3 |

|Y |15 |12 |9 |

|X |5 |4 |3 |

a) y= x + 3 b) y = 3x c) d)

13. Mark has a total of 600 XBOX games. Of those games 1/3 is violent, out of the violent games 30% use bad language, and out of those games (violent and bad language), 3/5 have are extremely inappropriate. How many games were considered extremely inappropriate?

Theoretical Predictions CLASSWORK Day 13

EXPERIMENTAL PROBABILITY: Determined by OBSERVING and COUNTING outcomes from a sample. This is what ACTUALLY happens!

THEORETICAL PROBABILITY: Determined by what we EXPECT will happen.

Example:

How many times would you EXPECT to get a B if you spun the spinner 4 times?

To get a B – your chances are[pic]. So multiply the 4 times by [pic] to get your answer of 1.

1. How many times would you EXPECT to get a C if you spun the spinner to the right:

a) 4 times b) 100 times c) 200 times d) 1,000 times

2. How many times would you EXPECT to get an A,B, or C if you spun the above spinner:

a) 4 times b) 52 times c) 64 times d) 100 times

Which letter will the spinner most likely land on? _______ Explain _____________________________

3. How many times would you EXPECT to get a 5 if you rolled the die:

a) 6 times b) 36 times c) 132 times d) 6,000 times

4) A company that produces car parts tests a sample of fifty parts. After testing all fifty parts, they find that 7 parts are defective.

a) What is the experimental probability of a part being defective?

b) How many defective parts would you expect in a batch of 1000 parts?

c) How could the company find a more accurate representation of their defective parts?

5) A school has 1,060 students. The results of a survey are shown.

|Students Surveyed |Students Who Produced Computer Art |

|40 |24 |

If the trend in the table continues, which is the best prediction of the total number of students who produced computer art?

A) 260 students B) 480 students C) 640 students D) 790 students

6) The quality control engineer of Top Notch Tool Company finds flaws in 8 of 60 wrenches examined. Predict the number of flawed wrenches in a batch of 2,400.

Theoretical Predictions HOMEWORK Day 13

1) Find the experimental probability for Seneca Boys Basketball Team. P(loss) =

Wins: 22 Losses: 3

2) A quality control engineer at a factory inspected 300 glow sticks for quality. The engineer found 15 defective glow sticks. What is the experimental probability that a glow stick is defective? How many glow sticks would the engineer expect to find defective out of 900?

3) A quality control inspector finds flaws in 6 of 45 tools examined. If the trend continues, what is the best prediction of the number of defective tools in a batch of 540?

4) The population of Los Angeles, California, throughout the 20th century is shown in the table to the right.

Between which 2 years did the population increase the most?

Answer between ________________ and _______________________

Based on the data in the table, predict the population of Los Angeles in

the year 2020. Justify your prediction.

Review

5) During hockey practice, Dane blocked 19 out of 30 shots and Matt blocked 17 out of 24 shots. For the first game, the coach wants to choose the goalie with the greater probability of blocking a shot. Which player should he choose? ______________ Explain

6) After tax (8%), a Bose stereo system costs $5,400. Jim, the salesperson makes 5% commission on his sales. How much commission did Jim earn on his sale?

7) A diver’s elevation is decreasing at a rate of 30 feet per minute. If the diver starts at sea level, what will her elevation be after 2.5 minutes?

A. – 75 feet B. – 12 feet C. 12 feet D. 75 feet

Simulations Classwork Day 14

Vocabulary

Simulation –

Drought (in a problem below) -

How can you use technology simulations to estimate probabilities?

You can use a graphing calculator of a computer to generate random numbers and conduct a simulation.

Real World Application

1. A cereal company is having a contest. There are codes for winning prizes in 30% of it cereal boxes. Find an experimental probability that you have to buy exactly 3 boxes of cereal before you find a winning code.

Step 1 Choose a model.

The probability of finding a winning code is 30% = [pic]

Use the whole numbers from 1to 10. Let three numbers represent buying a box with a winning code.

Winning Code: 1, 2, 3 Non-winning code: 4, 5, 6, 7, 8, 9, 10

Step 2 Generate random numbers from 1 to 10 until you get one that represents a box with a winning code. Record how many boxes you bought before finding a winning code.

Ex. If five numbers are generated: 9, 6, 7, 8, 1 1 Represents a winning code

|Trial |Numbers Generated |Boxes Bought |

|1 |9, 6, 7, 8, 1 |5 |

|2 |2 |1 |

|3 |10, 4, 8, 1 |4 |

|4 |4, 10, 7, 1 |4 |

|5 |2 |1 |

|6 |4, 3 |2 |

|7 |3 |1 |

|8 |7, 5, 2 |3 |

|9 |8, 5, 4, 8, 10, 3 |6 |

|10 |9, 1 |2 |

Step 3 Perform multiple trials by repeating step 2

Step 4 Find the experimental probability

Look at the simulation and see that 1 of 10 trials, you

bought exactly 3 boxes of cereal before finding a winning code.

The experimental probability is [pic] or 10%.

Practice

1. There is a 30% chance that Chris’s county will have a drought during any given year. He performs a simulation to find the experimental probability of a drought in at least 1 of the next 4 years.

Chris’s model involves the whole numbers from 1-10. Complete the description of his model.

Let the numbers 1 to 3 represent ______________ Let numbers 4 to 10 represent ___________________

Perform multiple trials generating ______ random numbers each time.

Look at the results below and complete the tables.

|Trial |Numbers Generated |Drought Years |

|1 |10, 3, 5, 1 | |

|2 |10, 4, 6, 5 | |

|3 |3, 2, 10, 3 | |

|4 |2, 10, 4, 4 | |

|5 |7, 3, 6, 3 | |

According to the simulation, what is the experimental probability that there will be a drought in the county in at least 1 of the next 4 years?

Simulations Day 14 Homework

Try this:

John has to complete a research project on the ape

population in Spain. He is trying to estimate the size of

population of apes. He randomly catches 37 apes and

marks them with paint. He releases apes in jungle. The

following year he observes 250 apes and he found

that 10 were marked with the paint that

he used. Find out the best estimate for the size of the ape population?

-----------------------

Impossible

Equal Chance

Certain

[pic]

[pic]

[pic]

1

0

Very

Likely

Somewhat Likely

What is your favorite Sport?

Not Fair

|Pasta |Number |

|Macaroni |38 |

|Spaghetti |56 |

|Rigatoni |12 |

|Lasagna |44 |

1. Is Mr. Coffey’s sample biased?

2. What could he have done differently?

Discuss…What if Mr. Coffey arrives at school early one morning? He surveys the first 50 students who arrive at school. Is this a good sample that is likely to be representative? Explain

5

6

9

4

7

8

If the MAD is small, it means the data are bunched closely together. If the MAD is large, it means the data are spread out and have greater variability.

Mean Height

|Data point, x |mean |absolute deviation from mean |absolute |

| | |[pic] |deviation |

| | | | |

| | | | |

| | | | |

Basketball Team

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

Soccer Team

65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84

0 1 2 3 4 5 6

8 9 10 11 12 13 14

0 10 20 30 40 50 60

Based on the data above, which runner do you think runs at a more consistent pace? Explain.

Is their overlap? Yes or No If so, describe the overlap of the above data.

13 14 15 16 17 18 19

13 14 15 16 17 18 19

Stephen

John

0 1 2 3 4 5 6

0 1 2 3 4 5 6

0 1 2 3 4 5 6

Inference 1:

Inference 2:

Inference 3:

Inference 4:

Math Class

Science Class

0 5 10 15 20 25 30

Best Buy

50 55 60 65 70 75 80 85 90 95 100

Target

Inference #1 ______________________________________________________________________________________

Inference #2 ______________________________________________________________________________________

Inference #3 ______________________________________________________________________________________

78 79 80 81 82 83 84 85 86 87 88

City 1

78 79 80 81 82 83 84 85 86 87 88

City 2

Treetop Tours

Zip Adventures

20 30 40 50 60 70 80 90 100 110 120

28 29 30 31 32 33 34 35 36 37 38

28 29 30 31 32 33 34 35 36 37 38

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4) The histogram shows the number of directors and the number of movies they complete in a year. Find the difference between the directors who made 3 to 4 movies in a year and who made 5 to 6 movies in a year.

5) How many directors made 3 - 4 movies?

6) How many directors made at least 7 movies?

1) How many students scored at least an 81 on the test?

2) How many students scored less than and 81 on the

exam?

3) Can you determine the highest grade from the

Histogram? Explain.

4) How many students received a grade of 51?

Interval

*Overall, the girls’ heights are lower than the boys’ heights. Girl’s Mean(65) < Boy’s Mean(69)

*The girls’ heights are more consistently grouped together than the boys’ heights. Girls’ MAD(0.8 )< Boys’ MAD(1.4)

Total Outcomes:_______

Certain

0

Impossible

likely

unlikely

Equal Chance

1

[pic]

[pic]

[pic]

2

1

3

4

4 suits

c. Spades (black)

i. [pic] [pic]

d.

L

B

G

A

E

Z

K

O

Sum

# of rolls

A

A

A

B

B

D

C

C

|Trial |Numbers Generated |Drought Years |

|6 |8, 4, 8, 5 | |

|7 |6, 2, 2, 8 | |

|8 |6, 5, 2, 4 | |

|9 |2, 2, 3, 2 | |

|10 |6, 3, 1, 5 | |

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