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. Assume that GMAT scores are bell-shaped with a standard deviation of 100.

a. What is the z-score associated with a GMAT score of 347?
b. What percentage of GMAT scores are between 347 and 547?
c. Would a GMAT score of 340 be considered an outlier? Why or why not?

In a GMAT score distribution, a score of 347 has a z-score of -2, approximately 47.72% of scores lie between 347 and 547, and a score of 340 would be considered an outlier because it is more than 2 standard deviations away from the mean.

Explanation:

To answer your questions:

a. The z-score is calculated using the formula z = (X - μ) / σ where X is the score, μ is the mean score, and σ is the standard deviation. Thus for a GMAT score of 347, the z-score would be z = (347 - 547) / 100 = -2.

b. The percentage of GMAT scores between 347 (or -2 standard deviations) and 547 (the mean) on a bell curve is approximately 47.72% (this is the area from -2 to 0 on a standard normal distribution table).

c. Since an outlier is typically considered to be a data point that is located outside 1.5 times the interquartile range above the third quartile, or below the first quartile, a score of 340 is 2.07 standard deviations away from the mean in this case, so it can be considered an outlier.

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