Question

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Reyna got a score of 75.3; this version has a mean of 69.3 and a standard deviation of 12. Kaitlyn got a score of 228.4; this version has a mean of 206 and a standard deviation of 28. Cade got a score of 7.88; this version has a mean of 7.2 and a standard deviation of 0.4. 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, Cade 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.

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?

Whoever had the higher z-score.

Reyna:

Reyna got a score of 75.3; this version has a mean of 69.3 and a standard deviation of 12.

This means that
`X = 75.3, \mu = 69.3, \sigma = 12`

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

`Z = (75.3 - 69.3)/(12)`

`Z = 0.5`

Kaitlyn:

Kaitlyn got a score of 228.4; this version has a mean of 206 and a standard deviation of 28.

This means that
`X = 228.4, \mu = 206, \sigma = 28`

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

`Z = (228.4 - 206)/(28)`

`Z = 0.8`

Cade:

Cade got a score of 7.88; this version has a mean of 7.2 and a standard deviation of 0.4. This means that
`X = 7.88, \mu = 7.2, \sigma = 0.4`

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

`Z = (7.88 - 7.2)/(0.4)`

`Z = 1.7`

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