Question

Assume that the GMAT scores across the U.S. follow a bell shaped distribution (symmetric and unimodal) with mean 549 and standard deviation 76. Use the Empirical Rule (68-95-99.7 rule) to answer the following question: What is the GMAT score corresponding to the 16th percentile

Answer 1

The GMAT score corresponding to the 16th percentile is 473.

Explanation:

Empirical Rule.

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

68% of the measures within 1 standard deviation of the mean.

This means that they are between the 50 - (68/2) = 50 - 34 = 16th percentile(one standard deviation below the mean) and the 50 + (68/2) = 50 + 34 = 84th percentile(one standard deviation above the mean).

In this question:

Mean of 549, standard deviation of 76.

16th percentile:

One standard deviation below the mean, so 549 - 76 = 473.

The GMAT score corresponding to the 16th percentile is 473.