Question

GMAT Exam Scores. The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100. a. What percentage of GMAT scores are 647 or higher? b. What percentage of GMAT scores are 747 or higher? c. What percentage of GMAT scores are between 447 and 547? d. What percentage of GMAT scores are between 347 and 647?

Answer 1

Answer:

a. 15.866%

b. 2.275%

c. 34.134%

d. 81.860%

Step-by-step explanation:

In this question, we shall be using the formula for z-score a couple of times.

Mathematically;

z-score = (score - mean)/SD

where mean = 547 and SD = 100

A. % of GMAT scores 647 or higher

Mathematically;

z-score = (647-547)/100 = 100/100 = 1

P( z ≥ 1) = 1 - P( z < 1)

= 1 - 0.84134 = 0.15866 which is same as 15.866%

B. % of GMAT scores 747 or higher

z-score = (747-547)/100 = 200/100 = 2

So the probability is P(z ≥ 2) = 1 - P( z <2) = 1- 0.97725 = 0.02275 which is same as 2.275%

C. between 447 and 547

z-score for 447 = (447-547)/100 = -100/100 = -1

For 547 = (547-547)/100 = 0/100 = 0

So the probability is;

P( -1 < z < 0) = P(z < 0) - P(z < -1) = 0.5 - 0.15866 = 0.34134 which is 34.134%

D. between 347 and 647

z-score for 347 = (347-547)/100 = -200/100 = -2

z-score for 647 = (647-547)/100 = 100/100 = 1

So the probability is;

P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.84134 - 0.02275 = 0.81859 = 81.86%