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.