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.

What proportion of students who take the GMAT are expected to score between 400 and 700 points?

The proportion of students expected to score between 400 and 700 on the GMAT is found by calculating the z-scores for 400 and 700, then using a normal distribution table or calculator to find the areas corresponding to these z-scores.

Explanation:

The question asks for the proportion of students expected to score between 400 and 700 points on the GMAT examination, which follows a normal distribution with a mean of 527 and a standard deviation of 112. To find this, we first calculate the z-scores for both 400 and 700:

For 400: z = (400 - 527) / 112 = -1.13
For 700: z = (700 - 527) / 112 = 1.54

Using a standard normal distribution table or calculator, we find the areas corresponding to these z-scores. The area between z = -1.13 and z = 1.54 gives us the proportion of students scoring between 400 and 700. Assuming proper normal tables or computational tools are used, one would find this proportion by subtracting the area beyond z = -1.13 from the area beyond z = 1.54.