Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council's GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112.

1. What is the probability of an individual scoring above 500 on the GMAT?
2. How high must an individual score on the GMAT in order to score in the highest 5%?

(Table for probability provided at the end of this homework)

To calculate the probability of scoring above 500 on the GMAT, use the standard normal distribution table. To determine the score needed to be in the highest 5%, find the corresponding z-score and solve for x.

Explanation:

To calculate the probability of an individual scoring above 500 on the GMAT, we need to find the area under the normal distribution curve to the right of 500. First, we standardize the score using the formula z = (x - mean) / standard deviation. In this case, z = (500 - 527) / 112 = -0.2411. Using the provided table, we can find that the probability is approximately 0.4052.

Next, to determine the score required to be in the highest 5%, we need to find the z-score corresponding to that percentile. Using a standard normal distribution table or calculator, we find that the z-score for the highest 5% is approximately 1.645. Rearranging the formula z = (x - mean) / standard deviation, we can solve for x to find the corresponding GMAT score: 1.645 = (x - 527) / 112. Solving for x gives us x ≈ 747. In order to score in the highest 5% on the GMAT, an individual must score approximately 747 or above.

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