Question

Suppose GRE Quantitative scores are normally distributed with a mean of 587 and a standard deviation of 152. A university plans to offer tutoring jobs to students whose scores are in the top 14%. What is the minimum score required for the job offer? Round your answer to the nearest whole number, if necessary.

Answer 1

The minimum score required for the job offer is 751.

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 = 587, \sigma = 152`

A university plans to offer tutoring jobs to students whose scores are in the top 14%. What is the minimum score required for the job offer?

This is the value of X when Z has a pvalue of 1-0.14 = 0.86. So it is X when Z = 1.08.

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

`1.08 = (X - 587)/(152)`

`X - 587 = 1.08*152`

`X = 751`

The minimum score required for the job offer is 751.