The Graduate Management Admission Test (GMAT) is a standardized exam used by man

Question

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. Make sure to use the empirical rule to answer these questions. a. What percentage of GMAT scores are 647 or higher? % b. What percentage of GMAT scores are 747 or higher (to 1 decimal)? % c. What percentage of GMAT scores are between 447 and 547? % d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)? %

Explanation / Answer

Answer:

The empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average.

a).

z value for 647, z=(647-547)/100 = 1

The empirical rule shows that 68% will fall within the first standard deviation.

Therefore (100-68)/2=16% fall 647 or higher.

b).

z value for 747, z=(747-547)/100 = 2

The empirical rule shows that 95% will fall within the two standard deviation.

Therefore (100-95)/2=2.5% fall 747 or higher

c).

z value for 447, z=(447-547)/100 = -1

The percentage of scores between mean and 1 sd below mean is 68/2

= 34%

d).

z value for 347, z=(347-547)/100 = -2

z value for 647, z=(647-547)/100 = 1

The percentage of scores between mean and 2 sd below mean is 95/2 =47.5

The percentage of scores between mean and 1 sd above mean is 68/2 =34

The required percentage = 47.5+34

=81.5%

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