Question

Suppose that test scores on the Graduate Management Admission Test (GMAT) are normally distributed with a mean of 530 and standard deviation of 75.

a. What GMAT score separates the highest 15% of the scores from the rest? Do not round intermediate calculations. Round your answer to the nearest whole number. GMAT score =

b. What GMAT score corresponds to the 97 percentile? Do not round intermediate calculations. Round your answer to the nearest whole number. GMAT score =

c. What GMAT score would 91% of the test takers be expected to score above? Do not round intermediate calculations. Round your answer to the nearest whole number.

GMAT score =

Answer 1

Solution:-

Given that,

mean = = 530

standard deviation = = 75

a) Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15  

= P(Z < z) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < 1.036 ) = 0.85  

z = 1.036

Using z-score formula,

x = z * +

x = 1.036 * 75 + 530

x = 607.7

x = 608

a) Using standard normal table,

P(Z < z) = 97%

= P(Z < z) = 0.97  

= P(Z < 1.881) = 0.97

z = 1.881

Using z-score formula,

x = z * +

x = 1.881 * 75 + 530

x = 671.08

x = 671

c) Using standard normal table,

P(Z > z) = 91%

= 1 - P(Z < z) = 0.91

= P(Z < z) = 1 - 0.91

= P(Z < z ) = 0.09

= P(Z < -1.341 ) = 0.09

z = -1.341

Using z-score formula,

x = z * +

x = -1.341 * 75 + 530

x = 429.43

x = 429