Question

Imagine that you are Director of Admissions at a prestigious university like CSUB. You have a pile of 20,000 applications in front of you and your office in the Administration Building is overflowing. You need a quick way to compare a lot of data for students in order to decide who to admit to CSUB. You turn all of the scores into z-scores (high school GPA, ACT and/or SAT score).

Based on their z-scores of high school GPA, rank the following applicants in order from most desirable (a) to least desirable (e).

z-scores = .97, -.25, .49, -1.15, .03

a)
b)
c)
d)
e)

2. If the mean high school GPA in your sample is 3.71 and the standard deviation is .14, what is the GPA of the people with z-scores of: (show your work)

a) z = 1.72, GPA = _________

b) z = -.96, GPA = _________

c) z = 2.14, GPA = _________

d) z = -1.65, GPA = _________

For the following questions(3,4,5): the sample mean is 3.71 and the standard deviation is.14

3. What percent of students had a GPA at 3.48 or above? (show your work)

4. What percent of students had a GPA between 3.43 and 3.72? (show your work)

5. What is the GPA of a student who scores at the 76th percentile? (show your work)

6. You realize that not everyone takes both the SAT and the ACT. You know that the mean for the SAT is 1000 with a standard deviation of 198. The mean for the ACT is 22 with a standard deviation of 5.7.

Choose one person from each group to admit to CSUB (show your work)

ACT = 27, SAT = 1250 (circle one)

ACT = 22, SAT = 985 (circle one)

ACT = 26, SAT = 1225 (circle one)

ACT = 18, SAT = 700 (circle one)

For questions 7 & 8 Assume the mean for the SAT is 1000 with a standard deviation of 198. The mean for the ACT is 22 with a standard deviation of 5.7.

7. As Director of Admissions, you are encouraged to allow people in school with an ACT of 26 or an SAT of 1200. However, if people exhibit special talents that could contribute to the University (e.g., art, music, athletics), you can admit students that have either an ACT of 19 or an SAT of 940.

As Director you want to maintain the highest standards possible. As Director, which standard (the SAT or ACT) would you prefer the students with special talents to make? Why? (Be sure to answer the why question)

8. As Director of Admissions, what would you recommend to fix this problem (i.e. the problem of the one test being easier to get in with, than the other) In other words, what would the admit raw score have to be for each test, for them to be considered equal? (hint: equate raw scores based on z-scores, show your work)

Answer 1

1)a) 0.97
b) 0.49
c) 0.03
d) -0.25
e) -1.15

2) mean = 3.71 and std = 0.14

a) Z= 1.72

Z= X- mean/ std

Z* std = X- mean

Z* std+ mean = X

Now put the values

1.72*0.14+3.71= X

GPA= 3.9508

By applying same above method we have

b) X = 3.5756

c) X= 4..0096

d) X= 3.479

3) mean= 3.71 and std = 0.14

percent of students had a GPA at 3.48 or above

Since μ=3.71 and σ=0.14 we have:

P ( X>3.48 )=P ( X−μ>3.48−3.71 )=P ( (X−μ)/σ>(3.48−3.71)/0.14)

Since Z=(x−μ)/σ and (3.48−3.71)/0.14=−1.64 we have:

P ( X>3.48 )=P ( Z>−1.64 )

Use the standard normal table to conclude that:

P (Z>−1.64)=0.9495= 94.95%

Note: I have done the first three questions. Please repost rest questions. Thank you:)