## The SAT is an exam that is used by many universities for admission. Suppose that the scores on the SAT mathematics exam have a normal distri

Question

The SAT is an exam that is used by many universities for admission. Suppose that the scores on the SAT mathematics exam have a normal distribution with mean 500 and standard deviation of 100. The statistics department identified students scoring in the top 4% of the SAT mathematics exam for recruitment. About what is the cutoff score for recruitment by the statistics department

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2 months 2021-10-09T03:14:43+00:00 1 Answer 0 views 0

## Answers ( )

The cutoff score for recruitment by the statistics department is 675.

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:

The Z-score measures how many standard deviations the measure is from the mean. 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 probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Cutoff score for the top 4%.

100-4 = 96th percentile, which is X when Z has a pvalue of 0.96. So X when Z = 1.75.

The cutoff score for recruitment by the statistics department is 675.