Answer to Question #219352 in Statistics and Probability for sai

Question

The distribution of grade point averages​ (GPAs) for medical school applicants of a certain year were approximately​ Normal, with a mean of 3.55 and a standard deviation of 0.34. Suppose a medical school will only consider candidates with GPAs in the top 20​% of the applicant pool. An applicant has a GPA of 3.83. Does this GPA fall in the top 20​% of the applicant​ pool?

Select the correct choice below and fill in the answer box to complete your choice.

​(Type an integer or decimal rounded to two decimal places as​ needed.)

A.Yes. The cutoff for the top 20​% is a GPA of

B.

No. The cutoff for the top 20​% is a GPA of

.

Answer 1

$P(Z<z)=0.8\to z=0.84.$

$\frac{x-3.55}{0.34}=0.84 \to x=3.55+0.84*0.34=3.84.$

B.

No. The cutoff for the top 20​% is a GPA of 3.84.