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, January 5, 2015). Assume that GMAT scores are bell-shaped with a standard deviation of 100.

. What percentage of GMAT scores are 647 or higher?

15.8

b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?

2.9

c. What percentage of GMAT scores are between 447 and 547 ?

25

d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?

Using the empirical rule, we know that 68% of data falls within one standard deviation of the mean; 95% of data falls within two standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.

This means from the mean to 1 standard deviation (σ) above is 34% of data; from the mean to 1 σ below is 34% of data; from 1 σ to 2σ above is 13.5% of data; from 1σ to 2σ below is 13.5% of data; from 2σ to 3σ above is 2.35% of data; from 2σ to 3σ below is 2.35% of data; more than 3σ above is 0.15% of data; and more than 3σ below is 0.15% of data.

647 is 1 σ above the mean. This means that we go from here above;

13.5+2.35+0.15 = 16%

747 is 2σ above the mean. This means that we go from here above:

2.35+0.15 = 2.5%

447 is 1σ below the mean and 547 is the mean. This means that we have 34%.

347 is 2σ below the mean and 647 is 1 above the mean. This means we go from:

13.5+34+34 = 81.5%