High School

The Graduate Management Admission Test (GMAT) is a standardized exam used by many colleges as part of the assessment for admission to graduate programs in business. The mean GMAT score is 522 with a standard deviation of 111. The dataset used to compute these statistics is negatively skewed. What percentage of GMAT scores are between 411 and 633?

Answer :

Around 68.26% of GMAT scores fall within the range of 411 and 633.

To find the percentage of GMAT scores between 411 and 633, we can use the Z-score formula.

First, we calculate the Z-scores for both values:
Z1 = (411 - 522) / 111 = -1
Z2 = (633 - 522) / 111 = 1

Next, we use a Z-table or calculator to find the cumulative probability associated with each Z-score:
P(Z < -1) = 0.1587
P(Z < 1) = 0.8413

To find the percentage between the two scores, we subtract the lower cumulative probability from the higher cumulative probability:
P(-1 < Z < 1) = P(Z < 1) - P(Z < -1)
P(-1 < Z < 1) = 0.8413 - 0.1587 = 0.6826

Therefore, approximately 68.26% of GMAT scores are between 411 and 633.

In conclusion, around 68.26% of GMAT scores fall within the range of 411 and 633.

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