Answer:
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.