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Mathematics

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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?

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Answer:

16% of GMAT scores are 647 or higher.

Step-by-step explanation:

Consider the provided information.

The average GMAT score is 547. Assume that GMAT scores are bell-shaped with a standard deviation of 100.

We need find the percentage of GMAT scores are 647 or higher.

[tex]z=\frac{\bar x-\mu}{\sigma}[/tex]

Substitute the respective values in above formula.

[tex]z=\frac{647-547}{100}[/tex]

[tex]z=\frac{100}{100}[/tex]

[tex]z=1[/tex]

According to the empirical rule 68% will fall within the first standard deviation.

100 - 68 = 32% of the provided data fall outside the first standard deviations of the mean. Also [tex]\frac{32}{2}[/tex] = 16% of the provided data fall below the first standard deviations of the mean.

Therefore, 16% of GMAT scores are 647 or higher.

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