Question

A college admissions officer evaluates potential students for acceptance based on many qualities, one of which is high school GPA.
(a) Student A has a high school GPA of 3.75. The high school GPA of students applying to this college is approximately Normal with a mean of 3.8 and a standard deviation of 0.08. Calculate and interpret the z-score for Student A.

(b) Student B’s high school GPA has a z-score of z = –0.875. If all else were equal and Student A and Student B were contending for the last open spot, which student should be offered admission?

(c) Student C’s high school GPA is at the 99th percentile among students applying to this college. What is the student’s high school GPA?

Answer 1

Answer:

A.)

3.75-3.8/.08  

-0.625 below the mean score

B.)

-0.875= x-3.8/.08

-.875*.08=x-3.8

-.07=x-3.8

x=3.73

Student B has a lower GPA (3.73) than student A (3.75)

Student A should be admitted.

C.)99th percentile z score = 2.326

2.326= x-3.8/.08

2.326 * .08=x-3.8

.186=x-3.8

x=3.986 or 3.99

Students GPA= 3.99

Step-by-step explanation: