The mean quantitative score on a standardized test for female college-bound high school seniors was 350. the scores are approximately normally distributed with a population standard deviation of 75. a scholarship committee wants to give awards to college-bound women who score at the 96th percentile or above on the test. what score does an applicant need? complete parts (a) through (g) below.

The applicant need a score of at least 481.25.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the percentile of this measure.

In this problem, we have that:

The mean quantitative score on a standardized test for female college-bound high school seniors was 350. The scores are approximately Normally distributed with a population standard deviation of 75. This means that .

A scholarship committee wants to give awards to college-bound women who score at the 96th percentile or above on the test. What score does an applicant need?

This score is the value of X when Z has a pvalue of 0.96.

Looking at the z score table, we find that Z has a pvalue of 0.96 at . So

The applicant need a score of at least 481.25.

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