Question

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1504 and a standard deviation of 300. The local college includes a minimum score of 1954 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement

Answer 1

6.68% of students from this school earn scores that satisfy the admission requirement

Explanation:

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

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

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:

`\mu = 1504, \sigma = 300`

The local college includes a minimum score of 1954 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement

This is 1 subtracted by the pvalue of Z when X = 1954. So

`Z = (X - \mu)/(\sigma)`

`Z = (1954 - 1504)/(300)`

`Z = 1.5`

`Z = 1.5` has a pvalue of 0.9332

1 - 0.9332 = 0.0668

6.68% of students from this school earn scores that satisfy the admission requirement