1 - JustAnswer



1. The theoretical probability of undesirable side effects resulting from taking Pyrene is 1 in 15. If 210 people take Pyrene to relieve congestion, theoretically how many will encounter undesirable side effects?

1/15 * 210

= 14 people

2. A bag contains 16 yellow marbles, 6 green marbles, and 7 red marbles. What is the chance of drawing a green marble? If a yellow marble is drawn the first time and then a second marble is drawn without replacement, what is the probability of drawing a red marble? Give solutions exactly in reduced fraction form, separated by a comma.

 

total = 16+6+7 = 29 marbles

Chance of green = 6/29

Change of red on the second time after a yellow (there are only 28 marbles left): 7/28 = 1/4

So the answers are:

6/29, 1/4

3. The odds in favor of Galloping Gary winning the horse race are 17:3. Determine the probability that Galloping Gary wins the horse race.

odds = p/(1-p)

17/3(1-p) = p

17/3 – 17/3p = p

17/3 = 20/3 p

17 = 20p

p = 17/20

       [pic]17/20

4. The odds against Methodical Mark winning the horse race are 13:2. Determine the probability that Methodical Mark wins the horse race.

odds against = (1-p)/p

13/2 = (1-p)/p

13/2 p = 1-p

15/2 p = 1

p = 2/15

       [pic]2/15

5. 

A mini license plate for a toy car must consist of a two numbers followed by a vowel. Each number must be a 3 or a 6. Repetition of digits is permitted.

1. Use the counting principle to determine the number of points in the sample space.

2 choices for the numbers, 5 choices for the letter

2*2*5 = 20

2. Construct a tree diagram to represent this situation and submit it to the week 5, assignment 2 drop box.

[pic]

3. List the sample space.

33A, 33E, 33I, 33O, 33U

36A, 36E, 36I, 36O, 36U

63A, 63E, 63I, 63O, 63U

66A, 66E, 66I, 66O, 66U

4. Determine the exact probability of creating a mini license plate with a 3. Give solution exactly in reduced fraction form.

 There are 20 total choices.

15 have a “3”:

15/20

= 3/4

6. A factory worker places 62 newly created circuits on a shelf to be checked for quality. Of these, 5 will not work correctly. Suppose that she is asked to randomly select two circuits, without replacement, from the shelf. What is the chance that both circuits she selects will be defective? Show step by step work! Approximate the solution to the nearest ten thousandth.

 

First circuit defective: 5/62

Now there are 61 boards, and 4 defective ones: 4/61

Multiply these:

5/62 * 4/61

= about 0.0053

7. The FM Radio stations with high signal strength in New Orleans break down into the following categories:

|Hip hop |2 |

|Religious |6 |

|Country |2 |

|Rock |3 |

|Talk Radio |2 |

|Other |5 |

 

If someone driving in New Orleans tuned into an FM radio station with high signal strength at random, what would be the chances he would get a Hip hop or Talk Radio station? Give answer as a fraction in lowest terms.

 

total = 2+6+2+3+2+5 = 20

hip hop + talk radio = 2+2 = 4

Fraction = 4/20

= 1/5

8. The pets a particular veterinarian saw yesterday break down into the following categories:

|Cats |10 |

|Dogs |18 |

|Bird |4 |

|Ferret |3 |

|Lizard |1 |

 

If there is one folder per pet and Valerie selected a folder at random from yesterday’s stack of folders, what would be the chances she would not get a lizard’s chart? Give answer as a fraction in lowest terms.

 

total = 10+18+4+3+1 = 36

Not lizard = 35

Prob = 35/36

9. If casino five card stud were fair, how much should it pay to a player who bets $10 and gets a straight flush versus a dealer who gets two pair? The odds against getting a straight flush in five card stud are about 64974 to 1. 

 

Multiply the odds by the bet:

10*64974

= $649740

1. Of 31 college seniors at Southern Swampland University, 17 preferred pepperoni pizza, 12 preferred supreme, and 2 preferred cheese. If we picked a college senior at Southern Swampland University at random, theoretically what is the probability that he or she would prefer supreme? Give solution exactly in reduced fraction form.

 

Supreme/total

= 12/31

2. A bag contains 8 pink marbles, 5 green marbles and 10 brown marbles. What is the chance of drawing a green marble? If a green marble is drawn then placed back into the bag, and a second marble is drawn, what is the probability of drawing a brown marble? Give solutions exactly in reduced fraction form, separated by a comma.

 

total = 8+5+10 = 23

Prob green = 5/23

Second part, since there is replacement, the first draw doesn’t matter: 10/23

So:

5/23, 10/23

3. A police officer’s work responsibilities include street patrols, questioning suspects and preparing suspect files. On Monday, Mona, a police officer, spent 6 hours on street patrol, 1 hour questioning suspects and 2 hours preparing suspect files. If Mona’s work hours on Tuesday are spent approximately the same way they were on Monday, what are the chances that at any given moment on Tuesday Mona will be questioning suspects or preparing suspect files? Show step by step work! Give answer as a fraction in lowest terms.

 

total = 6+1+2 = 9

Prob = (questioning+files)/total = (1+2)/9 = 3/9 = 1/3

4. According to the U. S. Census Bureau, the total 2008 U.S. population was 303,824,640. The chart below summarizes the 2008 population for five U.S. States.

 

|State |2008 Population |

|Missouri |5,911,605 |

|Pennsylvania |12,448,279 |

|Tennessee |6,214,888 |

|Utah |2,736,424 |

|Washington |6,549,224 |

 

SOURCE: U. S. Census Bureau

 

What is the probability that a randomly selected U.S. resident did not live in Washington?  Show step by step work. Round solution to the nearest thousandth.

 

= (total-Washington)/total

= (303824640-6549224)/303824640

= 0.978

5. 

A mini license plate for a toy car must consist of a one digit odd number followed by two letters. Each letter must be a J or Q. Repetition of letters is permitted.

1. Use the counting principle to determine the number of points in the sample space.

there are 5 odd digits and 2 letters:

5*2*2 = 20

2. Construct a tree diagram to represent this situation and submit it to the week 5, assignment 3 dropbox.

[pic]

3. List the sample space.

1JJ, 1JQ, 1QJ, 1QQ

3JJ, 3JQ, 3QJ, 3QQ

5JJ, 5JQ, 5QJ, 5QQ

7JJ, 7JQ, 7QJ, 7QQ

9JJ, 9JQ, 9QJ, 9QQ

4. Determine the exact probability of creating a mini license plate with a J. Give solution exactly in reduced fraction form.

 15 out of the 20:

15/20

Simplify:

3/4

6. For a trip a woman packed 6 tops, 7 skirts, and 4 pairs of shoes. How many different outfits can she wear?

 

multiply:

6*7*4

= 168

7. 

A card is selected from a standard deck of 52 playing cards. Find the probability of selecting

 

1. a prime number under 10 given the card is red. (1 is not prime.)

the primes are: 2, 3, 5, 7 (for hearts and also for diamonds)

There are 26 red cards. There are 8 primes.

8/26

= 4/13

2. a King, given that the card is not a heart.

There are 39 non-hearts. There are 3 Kings that aren’t hearts:

3/39

= 1/13

3. a nine given the card is a face card. (An ace is not a face card.)

There are no nines that are face cards.

P = 0

 

Show step by step work. Give all solutions exactly in reduced fraction form.

 

8. 

Last fall, a gardener planted 95 iris bulbs. She found that only 80 of the bulbs bloomed in the spring.

 

1. Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms.

80 bloom out of 95:

80/95

Simplify:

16/19

2. How many of the bulbs should she plant next fall if she would like at least 91 to bloom?

 divide:

91 / (16/19)

= 108.0625

Rounds up to:

= 109

9. In how many ways can 10 instructors be assigned to eight sections of a course in mathematics?

 

Assuming each section is the same, and order doesn’t matter.

10 choose 8

= 10! / (8! * 2!)

= (10*9) / (2*1)

= 45

10. 

Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma.

 

drawing a red five out of a standard 52 card deck given it’s not a face card or an ace.

rolling a total of 3 on two fair six sided dice

11. In how many different ways can the top eleven new indie bands be ranked on a top eleven list? The top hit song for each of the eleven bands will compete to receive monetary awards of $1000, $500, $250 and $100, respectively. In how many ways can the awards be given out?

 

First part:

11! = 39916800

Second part:

11*10*9*8 = 7920

12. How many different ways are there for an admissions officer to select a group of 8 college candidates from a group of 12 applicants for an interview?

12 choose 8

12! / (8! * 4!)

= 495

1. Given the situation described, identify the type of sampling involved. A local library polls every 9th customer about the selection of periodicals offered.

       [pic]systematic sampling

 

2. A magazine article cited the numbers on household income in Berea, KY as given by the U.S. Census Bureau. Was a sample or the population used?

 

population – the census looks at the entire population

3. A medical equipment manufacturing company tested the reliability of a medical apparatus.

It measured the time to failure of 16 randomly sampled machines it produced. Listed below are the 16 measurements (in months) for the time to first failure.

19    34    36    23    34    27    19    15    19    41

7     27    7     13    16    12

 

From this data, find the sample mean, median, mode and midrange for this data. Round each to the nearest tenth, if needed. Include units with each answer.

 

From excel:

mean = 21.8

Median = 19

Mode = 19

Midrange = 24

4. The mean household incomes of randomly selected residents of Las Vegas, Nevada in U.S. dollars are listed.

 

$61,050     $59,250     $77,100     $46,720     $78,500

$51,150     $48,000     $45,120     $51,150    

 

From this data set, find the sample mean, median, mode and range for the household incomes. Round each to the nearest dollar if necessary. Include units with each answer.

 

Which of the numbers you calculated is a better measure of the central tendency of the incomes given? Give a specific statistical reason for your conclusion.

 

mean = $57,560

Median = $51,150

Mode = $51150

Range = $33,380

The median is the best measure, because there are 4 values higher than it and 4 values lower than it.

4. Given the histogram below, create a grouped frequency distribution and submit it to the Week 6, Assignment 2 drop box.(Histogram file submitted)#5

 [pic]

 

|Time |Frequency |

|1 |1 |

|2 |0 |

|3 |1 |

|4 |1 |

|5 |1 |

|6 |1 |

|7 |2 |

|8 |1 |

|9 |0 |

|10 |1 |

6. Match the frequency diagram given with the correct histogram.

(The four histogram submitted)…

[pic]

 

| |Number of people |

|Average hours select residents of Davao, the Philippines, spent watching | |

|television each week | |

|0 - 2 |3 |

|3 - 5 |5 |

|6 - 8 |12 |

|9 - 11 |10 |

|12 - 14 |27 |

|total |57 |

7. The number of baby deliveries in a small hospital was sampled over 6 hour periods.  Below is the sample:

11    12    7     16    4     8     9     7     3     4    

9     4     6     12    9     8     4     6     12   

 

From this data set, compute the sample mean, median, mode and midrange. Compute the 1st

quartile and 3rd and interpret their meanings.

 

from excel:

Mean = about 7.95

Median = 8

Mode = 4

Midrange = 9.5

1st quart is the score that has 25% of the data below: 5

3rd quart is the score that has 75% of the data below: 10

8. The number of baby deliveries in a small hospital was sampled over 6 hour periods. Below is the sample:

 

33    36    21    48    12    24    27    21    9     12

27    12    18    36    27    24    12    18    36   

 

 

Construct a stem and leaf plot of the data.

 

0 | 9

1 | 2 2 2 2 8 8

2 | 1 1 4 4 7 7 7

3 | 3 6 6 6

4 | 8

9. Below are the blood types of 16 blood donors.

 

O-    A+    O-    O+    AB-   A-

A+    B+    O+    A+    B-    O+

A-    O+    B-    B+         

 

i.Make a frequency table using these 7 blood types: O+, O-, A+, A-, B+, B-, AB-

O+: 4

O-: 2

A+: 3

A-: 2

B+: 2

B-: 2

AB-: 1

ii.What is (are) the mode(s)?

The mode is O+, which appears the most times (four)

iii.Does it make sense to talk about the average for this data? Why or why not?

No, there cannot be an average for nominal data. You can’t average letters for blood types, since they have no numerical value.

iv.Using your frequency table draw a pie chart to display the distribution of blood types by filling in the following table:

|Type |Frequency |Percentage of total |Measure of Central Angle (in degrees) |

|O+ | 4 | 25 | 90 |

|A+ | 3 | 18.75 | 67.5 |

|B+ | 2 | 12.5 | 45 |

|O- | 2 | 12.5 | 45 |

|A- | 2 | 12.5 | 45 |

|AB- | 1 | 6.25 | 22.5 |

|B- | 2 | 12.5 | 45 |

[pic]

Submit your solutions to the Week 6, Assignment 2 dropbox.

  (Points: 12)

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