Question

Last year freshmen class totaled 5,305 students. Of these 1,258 received a merit scholarship to help offset the cost. The amount a student received was N(3,456, $478). If the cost of the full tuition was 4,250 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition? Round answer to the nearest whole percent.

A. 12%
B. 18%
C. 24%
D. 30%

Answer 1

Using the z-score, we find that approximately 95.15% of students received scholarships below the full tuition cost. Therefore, about 4.85% of students did not receive enough to cover full tuition. Given answer choices do not accurately reflect this percentage, indicating a possible mistake.

Step-by-step explanation:

The question asks what percentage of students who received a merit scholarship did not receive enough to cover full tuition. The full tuition cost was $4,250, and the merit scholarship was normally distributed with an average of $3,456 and standard deviation of $478. To determine the percentage of students who did not receive enough to cover tuition, we need to find the proportion of the normal distribution that falls below the full tuition cost.

First, we calculate the z-score for the cost of full tuition:
Z = (X – mean) / SD = (4250 – 3456) / 478 ≈ 1.66

Looking at the z-score table, a z-score of 1.66 corresponds to a cumulative proportion of about 0.9515. This means approximately 95.15% of the distribution falls below the full tuition cost. To find the percentage that did not receive enough to cover tuition, we subtract this value from 100%:

100% - 95.15% = 4.85%

Since the percentage is closer to 4.85%, none of the given options A. 12%, B. 18%, C. 24%, D. 30% are correct. There seems to be a mistake as the nearest whole percent should be 5%, which is not listed.