Answer to Question #219739 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 0.33. Suppose a medical school will only consider candidates with GPAs in the top 20​% of the applicant pool. An applicant has a GPA of 3.84. 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 blank

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

Answer 1

Let X the random variable that represents the grade point averages (GPAs) for medical school applicants of a certain year of a population, and for this case we know the distribution for X is given by:

X~N(3.55,0.33)

$\mu=3.55 \\ \sigma= 0.33$

The best way to solve this problem is using the normal standard distribution and the z score given by:

$Z = \frac{x - \mu}{\sigma}$

We want to find a value a, such that we satisfy this condition:

$P(X<a)=0.80 \\ P(Z< \frac{a- \mu}{\sigma}) = 0.80 \\ \frac{a- 3.55}{0.33} = 0.842 \\ a = 3.55+0.33 \times 0.842 = 3.827$

So the score that separates the bottom 80 % of data from the top 20 % is 3.827. Since the value obtained by the applicant is 3.84 >3.827 falls on the top 20 %.

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