The distribution of grade point averages (GPAs) for medical school applicants of a certain year were approximately Normal, with a mean of 3.48 and a standard deviation of 0.36. Suppose a medical school will only consider candidates with GPAs in the top 20% of the applicant pool. An applicant has a GPA of 3.75. Does this GPA fall in the top 20% of the applicant pool?

Question

The distribution of grade point averages​ (GPAs) for medical school applicants of a certain year were approximately​ Normal, with a mean of 3.48 and a standard deviation of 0.36. Suppose a medical school will only consider candidates with GPAs in the top 20​% of the applicant pool. An applicant has a GPA of 3.75. Does this GPA fall in the top 20​% of the applicant​ pool?

BlackTom AI · Accepted Answer

To determine whether an applicant with a GPA of 3.75 falls in the top 20% of the distribution, we first identify the cutoff for the top 20%. Since GPAs are approximately normally distributed with mean μ = 3.48 and standard deviation σ = 0.36, the 80th percentile corresponds to a z-score around 0.84 (more precisely 0.8416).

Now convert that z-score to an actual GPA: cutoff = μ + z·σ = 3.48 + 0.8416×0.36 ≈ 3.48 + 0.303 = 3.783. This means about 20% of applicants have GPAs above approximately 3.783.

Option A: Yes. The statement would be true only if 3.75 were at or above the 80th percentile cutoff. Since 3.75 ≈ 3.75 is less than 3.783, it does not reach the cutoff. Therefore this option is incorrect.

Option B: No. Given the calculated cutoff of roughly 3.783, a GPA of 3.75 lies below the threshold required to be in the top 20%, so the applicant would not be among the top fifth applicants. This option is correct.

In summary, comparing 3.75 to the 80th percentile cutoff shows 3.75 is slightly below the cutoff, confirming that the GPA does not place in the top 20%.

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