Answer :
We must first identify the z-score that corresponds to a GMAT score of 747 in order to use the empirical rule.
How can it be explained in detail?
The formula can be used to do this:
z = (747 - 547) / 100, z = 2
The empirical rule, which is the next step, asserts that:
The data is within one standard deviation of the mean for around 68% of the time.
The data is within two standard deviations of the mean for around 95% of the time.
99.7% of the data is contained within three standard deviations of the mean.
Therefore, if a z-score of 2 equals a GMAT score of 747, we may deduce the following:
2.5% of GMAT scores are more than 747 (100% - 97.5%).
The percentage of GMAT scores exceeding 747 + 2 * 100 (100% - 99.85%) is about 0.15 percent.
Therefore, we may estimate that 7.47 or higher GMAT scores make up around 2.5% of all GMAT results.
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Final answer:
Approximately 2.5% of GMAT scores are 747 or higher.
Explanation:
To answer this question, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, approximately 68% of the GMAT scores fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.
With an average GMAT score of 547 and a standard deviation of 100, we can calculate the standard deviation above the mean as follows: (747 - 547) / 100 = 2 standard deviations.
Therefore, using the empirical rule, we can estimate that only about 2.5% of GMAT scores would be 747 or higher.
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