Day
Geo X Name _____________________________
Unit 16; Day 1 Date ______________________________
Day 1 Homework Worksheet A
Making and Reading Graphs
The graph to the right shows the distribution of IQ scores for a group of 60 students. Use it to answer questions
1. What is the shape of the distribution?
2. What does the shortest bar on the histogram tell you? Be specific.
3. Estimate the number of students who scored between 105 and 135 on the IQ tests.
The back – to – back stem plot to the right shows the number of caesarean-sections performed by 15 male doctors and 10 female doctors in Switzerland in a single year. Use the stemplot to answer questions 4-6.
4. What does the entry 3|3 on the female side of the plot represent? (Be specific.) Hint: remember that there are 10 female doctors.
5. What are the “typical” number of caesareans performed by the two groups? What does this tell you about male OB’s vs female OB’s in Switzerland?
6. Find the maximum and minimum number c-sections for each of the two groups.
Male Docs: Female Docs:
Max = Max =
Min = Min =
Twenty students were asked how long their commute to school was (in minutes) each day. The asnwers given are provided in the table below.
|8 |13 |
|0 |5 8 8 9 9 |
|1 | |
|1 | |
|2 | |
|2 | |
|3 | |
|3 | |
7. A split stem plot can be used when a set of data is clumped too tightly to adequately see the distribution. Finish the split stemplot that has been started on the right. Notice that each “stem” is split so that values ending in 0-4 are placed in the first branch and those ending in 5 – 9 are placed in the second branch.
8. Describe the shape of the completed stem plot.
9. The stemplot should appear to have two distinct groups of times of students’ commutes to school. Speculate as to a reason that a student may fall into one group or the other. (Think about how people may get to school.)
10. What is the “typical” commute time for students?
The ages of a sample of 20 children at a performance of Disney on Ice are shown below.
|2 |2 |3 |
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Total the last column =
Divide the total by the number of numbers (which is 5) = This is the variance.
Find the square root of the variance.
Standard Deviation = ______________
5. A clerical error led to one of the player’s weights being recorded incorrectly. His weight is actually 220 rather than 120. Describe the effect that the correction will have on the mean and standard deviation.
The following heights were recorded for 7 trapeze artists: (in cm)
175 182 190 180 192 186 190
6. Write the numbers in order:
7. Find the range.
8. Find the mean.
9. Find the standard deviation using the table.
|[pic] heights |[pic] |[pic] |
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Total the last column =
Divide the total by the number of numbers (which is 7) = This is the variance.
Find the square root of the variance.
Standard Deviation = ______________
10. Which of the following 2 data sets has the largest standard deviation? Why?
a. 65, 75, 85, 95 b. 110, 112, 114, 116
Geo X Name _____________________________
Unit 16; Day 4 Date ______________________________
Day 4 Homework Worksheet D
z-scores and Relative Position
1. The means and standard deviations of the SAT subject tests for 3
languages are given in the following table:
|Subject |Spanish |German |Latin |
|Mean |679 |658 |616 |
|Standard Deviation |35 |31 |29 |
a. Find the z-score for each of the following students:
James took the German exam and scored 680.
Laura took the Latin exam and scored 610.
Patty took the Spanish exam and scored 690.
Scott took the Latin exam and scored 650.
Martin took the Spanish exam and scored 650.
Suzanne took the German exam and scored 620.
b. Who had the highest relative score on their SAT subject test? Why?
c. Who had the lowest relative score on their SAT subject test? Why?
2. Arnold and Margret at twins. At 6 months, Arnold weighed 16 pounds and Margaret weighed 15.5 pounds. The mean weight for 6 month old boys is 16.75 pounds with a standard deviation of 2 pounds. The mean weight for 6 month old girls is 15 pounds with a standard deviation of 1.8 pounds. Which one of the twins weighs more, relative to other babies of the same gender?
3. Raw scores on behavioral tests are often transformed for easier comparison. A test of reading
ability has a mean of 75 and a standard deviation of 10 when given to third-graders. Sixthgraders
have a mean score of 82 and a standard deviation of 11 on the same test. David is a third-grade student who scores 78 on the test. Nancy is a sixth-grade student who scores 81. Calculate the z-score for each student. Who scored higher within his or her grade?
4. Lamar is shopping for a used car, and he’s interested in determining the typical mileage on cars that are three or four years old. He looks at an online car-buying site and compares the number of miles on 30 cars that are three years old to 30 cars that are four years old. His results are summarized by Minitab below. All values are in thousands of miles. One car that Lamar is interested in is four years old and has been driven 40 thousand miles. Another one is three years old and has 30 thousand miles on it. How does the number of miles on these cars compare, relative to other cars of the same age?
[pic]
Geo X Name _____________________________
Unit 16; Day 5 Date ______________________________
Day 5 Homework Worksheet E
The Empirical Rule
1. The mean score on a standardized state test is 1180 with a standard deviation of 80 points.
a. Use the normal curve to mark the mean and find the values for 1, 2 and 3 standard
deviations on either side of the mean. Write these values on the axis.
b. What percent of students earned
between 1100 and 1260 on the exam? _____________
c. What percent of students earned
between 1020 and 1340 on the exam? _____________
d. What percent of students earned above a 1260? _____________
e. What percent of students earned below a 1020? _____________
f. What percent of students earned above 1180? ____________
g. What score would a student need to be in the lowest 16% of scores? ___________
2. A fire company in a rural community has a mean response time of 20 minutes with a standard
deviation of 5 minutes. The response times are normally distributed.
a. Use the normal curve to mark the mean and find the values for 1, 2 and 3 standard
deviations on either side of the mean. Write these values on the axis.
b. 68% of all response times fall between ___________ and __________ minutes.
c. 95% of all response times fall between ___________ and __________ minutes.
d. 99.7% of all response times fall between __________ and __________minutes.
e. Find the z-score for an emergency with a response time of 28 minutes.
f. Why can we not use the Empirical rule for the z-score found in question e?
g. If an emergency had a response time of 45 minutes, would you be surprised? Explain
your answer.
Geo X Name _____________________________
Unit 16; Day 6 Date ______________________________
Day 6 Homework Worksheet F
Standard Normal Calculations and the z-table
Multiple Choice: Circle the correct answer.
1. The area under the standard normal curve is equal to
a. 0.50 b. 0.99 c. 1.0 d. 2.0
2. The area to the left of z = 1.3 is
a. 0.1357 b. 0.5398 c. 0.8413 d. 0.9032
3. The area to the left of z = -0.2 is
a. 0.1151 b. 0.0179 c. 0.4207 d. 0.5793
4. The area to the right of z = 1.3 is
a. 0.9032 b. 0.50 c. 0.1587 d. 0.0968
5. Kitchen appliances don’t last forever. The lifespan of all microwave ovens sold in the United
States is approximately Normally distributed with a mean of 9 years and a standard deviation
of 2.5 years.
a. What is the z-score for a microwave oven that is 10 years old?
Round to the nearest tenth.
b. What proportion of microwave ovens are less than 10 years old?
c. What proportion of microwave ovens are greater than 10 years old?
6. A local post office weighs outgoing mail and finds that the weights of first-class letters is
approximately Normally distributed with a mean of 0.69 ounces and a standard deviation of 0.16
ounces.
a. Find the z-score for a letter that weighs 0.62 ounces. Round to the nearest tenth.
b. What proportion of letters weigh less than 0.62 ounces?
c. What proportion of letters weigh more than 0.62 ounces?
d. How much do the lightest 10% of letters weigh?
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