1)Tina's application for graduate school was ranked 67 out of 456 applications. Her twin sister's application to a different graduate school was ranked 17 out of 89 applications.

   a)  Which sister had the higher percentile ranking?

 

b)       If you had the data on the cumulative GPA of each student in each school in June 2019, which measure of average would be the most meaningful - mean, median, mode? Explain.

 

 

2)     A jury pool consists of 9 men and 11 women. The jury will be made up of 12 jurors. 

a.     If one person from among 5 court officers (3 women and 3 men) is chosen at random from to draw the names out of a hat, what is the probability that the person chosen to draw the names is a man?

b.     How many ways can the jury be formed if there are no restrictions on composition?

c.      How many ways can 8 women be chosen?

d.     How many ways can 4 men be chosen?

e.     What is the probability that the random selection of the jury will result in half women and half men?

1.

a. Comparing the percentile rank of Tina and her sister, Tina's percentile ranking is higher.

b. The most meaningful measure will be mean. 

2. 

a. The probability that a person chosen is a man is 0.5.

b. There are 125970 ways of forming a jury.

c. There are 165 ways of choosing 8 women.

d. There are 126 ways of choosing 4 men.

e. The probability of selecting half women and half men is 0.3081.

Step-by-step explanation

1. Tina's Rank : 67 out of 456

Sister's ranks : 17 out of 89

a. To find percentile ranking, use the following formula.

PercentileRank=YM?×100

M : Number of ranks at X

Y: Total number of ranks.

Tina's percentile = 67/456 * 100 = 14.7%

Tina's sisters' percentile rank = 17/89 * 100 =19.1%

Comparing the percentile rank of Tina and her sister, Tina's percentile ranking is higher.

b. The mean will give the numerical average of the cumulative GPA scores, while median will point out the middle value of scores when arranged in order and mode will give the GPA score which is scored by most of the students. The cumulative GPA is the average of all GPA scores. All the three measures of central tendency can be used to extract insights from the students' cumulative GPA scores. However, mean is considered the best measure since it accounts for all the scores in the data. Hence, mean will be the most meaningful measure for average.

2.

a. There are 6 court officers (3 women and 3 men)

P ( person chosen is a man ) = Number of men / Total court officers.

                                                = 3 / 6 = 0.5 

A jury pool has 20 people (9 men and 11 women). A jury is formed of 12 jurors.

b. The number of ways in which the jury can be formed is 20C12?=125970

c. Out of 11 women, the number of ways of choosing 8 women is 11C8?=165

d. Out of 9 men, the number of ways of choosing 4 men is 9C4?=126

e. Number of ways of selecting 6 men and 6 women is 9C6?×11C6?=38808

Here, there are half men and half women. 

P(half men and half women in the jury) = 20C12?9C6?×11C6??=12597038808?=0.3081