Question

two students are applying to a graduate school program at a highly competitive university. the admissions committee has to decide which one to admit. to do this, the committee looks at the students qualifications. in this case, the qualifications are equivalent except that the students took two different entrance exams. the chart, below, includes each students score on his or her exam. the chart also provides data about two normal distributions with a mean score and the standard deviation for each students entrance exam. if you were on the admissions committee, which student would you select and why? student a since his exam score is a higher number of standard deviations above the mean exam score than student b. student b since her exam score is a higher number of standard deviations above the mean exam score than student a. student a since his standard deviation is larger than that of student b. student b since her exam score was closer to the mean than student a.

Explanation:

Step1: Calculate z - score for Student A

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the student's score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For Student A: \(x = 448\), \(\mu=375\), \(\sigma = 32\)
\(z_A=\frac{448 - 375}{32}=\frac{73}{32}\approx2.28\)

Step2: Calculate z - score for Student B

For Student B: \(x = 272\), \(\mu = 247\), \(\sigma=20\)
\(z_B=\frac{272-247}{20}=\frac{25}{20}=1.25\)

Answer:

Student A since his exam score is a higher number of standard deviations above the mean exam score than Student B.