Question

Almost all medical schools in the United States require applicants to take the Medical College Admission Test (MCAT). On one exam, the scores of all applicants on the biological sciences part of the MCAT were approximately Normal with mean 8.9 and standard deviation 2.4. For applicants who actually entered medical school, the mean score was 10.1 and the standard deviation was 1.5.

(a) What percent of all applicants had scores higher than 13?
(b) What percent of those who entered medical school had scores between 9 and 12?

Answer 1

To find the percentage of applicants with scores higher than 13, calculate the z-score for 13 using the formula z = (x - µ) / σ. To find the percentage of those who entered medical school with scores between 9 and 12, calculate the z-scores for 9 and 12. Use a z-table to find the corresponding percentages.

Step-by-step explanation:

(a) To find the percentage of applicants with scores higher than 13, we need to calculate the z-score for 13 using the formula

z = (x - μ) / σ

where x is the score, μ is the mean, and σ is the standard deviation. Plugging in the values, we get

z = (13 - 8.9) / 2.4

= 1.46

Using a z-table, we can find that the percentage of applicants with scores higher than 13 is approximately 7.23%.

(b) To find the percentage of those who entered medical school with scores between 9 and 12, we need to calculate the z-scores for 9 and 12. Using the same formula as above, we get

z(9) = (9 - 10.1) / 1.5

= -0.73

z(12) = (12 - 10.1) / 1.5

= 1.27

Using a z-table, we can find that the area between -0.73 and 1.27 is approximately 66.28%. This means that approximately 66.28% of those who entered medical school had scores between 9 and 12.