Question

12. Most graduate schools of business require applicants for admission to take the Graduate

Management Admission Council's GMAT examination. Scores on the GMAT are
roughly normally distributed with a mean of 527 and a standard deviation of 112. What is
the probability of an individual scoring above 600 on the GMAT?
Show work here: (3 points)
112
23.7%.
527
415
627
Final answer:
2€
Final answer:
739
Go
25.7%
(2 points)
How high must an individual score on the GMAT in order to score in the highest
12%?
Show work here: (3 points)
600-527)
112
(2 points)

Answer 1

(a) 25.73%

(b) 658.6 or rounded to nearest integer 659 since gmat scores are in integers

Explanation:

Probability of scoring above 600
We can use standard normal tables and z value to compute the

First find the z score corresponding to 600 and compute the area to the right of the z score. This will be P(x > 600)

To find the z score use the formula

`z = (x - \mu)/(\sigma)`

where x = raw score = 600

μ = mean = 527

σ = standard deviation = 112

So we get

z = (600 - 527)/112 = 0.6518 rounded to 4 decimal places

P(x < 600) = P(z < 0.6518) which is the area to the left of 0.6518 from the standard normal tables

Using an online calculator such as calculator.net we find that P(z < 0.6518) works out to 0.74273

P(x > 600) = 1 - P(x < 600) = 1- 0.74273 = 0.25727 which corresponds to a percentage probability of 25.73%

Therefore the probability of an individual score above 600 on the GMAT is 25.73%

How high must an individual score in the GMAT to be in the highest 12 percentile

Here we are given the probability of scoring greater than a score as 12%

12% = 0.12

The z score for 0.12 in the standard normal table is found to 1.175

We can find this using a calculator or the standard normal table

Therefore in the formula for z we get
1.175 = (X - 527)/112

X - 527 = 1.175 x 112

X = 1.175 x 112 + 527 = 658.6 = 659 rounded

Therefore an individual must score at least 659 to be in the highest 12%