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 for a university is 521. Assume that GMAT scores are bell-shaped with a standard deviation of 50. If required, round your answers to one decimal place.

(a) What percentage of GMAT scores are 571 or higher?

(b) What percentage of GMAT scores are 621 or higher?

(c) What percentage of GMAT scores are between 471 and 521?

(d) What percentage of GMAT scores are between 421 and 571?

To find the percentage of GMAT scores that are 571 or higher, we need to calculate the standardized z-score. The z-score formula is given by: z = (x - mean) / standard deviation. Plugging in the values, we have z = (571 - 521) / 50 = 1. Using a standard normal distribution table, we can find that the percentage of scores that are 1 standard deviation above the mean is approximately 34.1%. Therefore, the percentage of GMAT scores that are 571 or higher is approximately 34.1%.

To find the percentage of GMAT scores that are 621 or higher, we again calculate the z-score: z = (621 - 521) / 50 = 2. Using the standard normal distribution table, we find that the percentage of scores that are 2 standard deviations above the mean is approximately 47.7%. Therefore, the percentage of GMAT scores that are 621 or higher is approximately 47.7%.

To find the percentage of GMAT scores that are between 471 and 521, we calculate the z-scores for both values: z1 = (471 - 521) / 50 = -1 and z2 = (521 - 521) / 50 = 0. We can then use the standard normal distribution table to find the area between these two z-scores, which is approximately 34.1% (the same as part a). Therefore, the percentage of GMAT scores that are between 471 and 521 is approximately 34.1%.

To find the percentage of GMAT scores that are between 421 and 571, we calculate the z-scores for both values: z1 = (421 - 521) / 50 = -2 and z2 = (571 - 521) / 50 = 1. Using the standard normal distribution table, we find that the area between these two z-scores is approximately 81.8%. Therefore, the percentage of GMAT scores that are between 421 and 571 is approximately 81.8%.

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