High School

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.

1. What percentage of GMAT scores are between 447 and 547?
2. What are the standard deviations of x and y?

Answer :

Final answer:

To find the percentage of GMAT scores between 447 and 547, calculate the z-scores and use the standard normal distribution table.

Explanation:

To find the percentage of GMAT scores between 447 and 547, we need to calculate the z-scores for both values and use the standard normal distribution table. The formula to calculate z-score is z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case, the mean is 547 and the standard deviation is 100.

For 447: z = (447 - 547) / 100 = -1

For 547: z = (547 - 547) / 100 = 0

Using the standard normal distribution table, we can find the percentage corresponding to each z-score. The percentage of GMAT scores between 447 and 547 is the difference between the two percentages.

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