Question

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14. Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16. Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?

Answer 1

Due to the higher z-score, Norma should be offered the job

Explanation:

Z-score:

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:

Whoever has the higher z-score should get the job.

Norma:

Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14.

This means that
`X = 84.2 \mu = 67.4, \sigma = 14`

So

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

`Z = (84.2 - 67.4)/(14)`

`Z = 1.2`

Pierce:

Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16.

This means that
`X = 276.8, \mu = 264, \sigma = 16`

So

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

`Z = (276.8 - 264)/(16)`

`Z = 0.8`

Reyna:

Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8.

This means that
`X = 7.62, \mu = 7.3, \sigma = 0.8`

So

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

`Z = (7.62 - 7.3)/(0.8)`

`Z = 0.4`

Due to the higher z-score, Norma should be offered the job