High School

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?

Answer :

Final answer:

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.