Question

Admission officers in Colleges A and B use SAT scores as their admis-sion criteria. SAT scores are normally distributed with mean 500 andstandard deviation 80. College A accepts people whose scores are above600, and College B accepts the top 1% of people in terms of their SATscores.(a) What percentage of high school seniors can get into College A

Answer 1

10.56% of high school seniors can get into College A

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 question, we have that:

`\mu = 500, \sigma = 80`

What percentage of high school seniors can get into College A

College A accepts people whose scores are above 600, so this is 1 subtracted by the pvalue of Z when X = 600. So

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

`Z = (600 - 500)/(80)`

`Z = 1.25`

`Z = 1.25` has a pvalue of 0.8944

1 - 0.8944 = 0.1056

10.56% of high school seniors can get into College A