Questions: 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 0.32. Suppose a medical school will only consider candidates with GPAs in the top 12% of the applicant pool. An applicant has a GPA of 3.79. Does this GPA fall in the top 12% 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 12% is a GPA of B. No. The cutoff for the top 12% is a GPA of

Solution Steps

To determine how the applicant's GPA compares to the mean, we calculate the Z-score using the formula:

\[ z = \frac{X - \mu}{\sigma} \]

where:

• \( X = 3.79 \) (applicant's GPA)
• \( \mu = 3.55 \) (mean GPA)
• \( \sigma = 0.32 \) (standard deviation)

Substituting the values:

\[ z = \frac{3.79 - 3.55}{0.32} = 0.75 \]

Thus, the applicant's Z-score is \( 0.75 \).

Next, we find the Z-score that corresponds to the top \( 12\% \) of the distribution. This is done using the inverse of the cumulative distribution function (CDF):

\[ z_{\text{cutoff}} = \text{norm.ppf}(1 - 0.12) \approx 1.1749867920660901 \]

Using the Z-score for the cutoff, we can find the GPA that corresponds to this Z-score:

\[ GPA_{\text{cutoff}} = \mu + z_{\text{cutoff}} \cdot \sigma \]

Substituting the values:

\[ GPA_{\text{cutoff}} = 3.55 + 1.1749867920660901 \cdot 0.32 \approx 3.93 \]

Now we compare the applicant's GPA of \( 3.79 \) to the cutoff GPA of \( 3.93 \):

\[ 3.79 < 3.93 \]

This indicates that the applicant's GPA does not fall within the top \( 12\% \) of the applicant pool.

Final Answer