Question

Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Tobias got a score of 84.584.5; this version has a mean of 66.966.9 and a standard deviation of 1111. Kiersten got a score of 281.8281.8; this version has a mean of 261261 and a standard deviation of 2626. Pierce got a score of 7.697.69; this version has a mean of 7.27.2 and a standard deviation of 0.70.7. 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

Tobias 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:

The applicant with the highest z-score should be chosen.

Tobias:

Score of 84.5, in a version with mean 66.9 and standard deviation 11. His z-score is found when
`X = 84.5, \mu = 66.9, \sigma = 11`

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

`Z = (84.5 - 66.9)/(11)`

`Z = 1.6`

Kiersten:

Score of 281.8, in a version with mean 261 and standard deviation 26. His z-score is found when
`X = 281.8, \mu = 261, \sigma = 26`.

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

`Z = (281.8 - 261)/(26)`

`Z = 0.8`

Pierce:

Score of 7.69, version with mean 7.2 and standard deviation 0.7. His z-score is found when
`X = 7.69, \mu = 7.2, \sigma = 0.7`.

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

`Z = (7.69 - 7.2)/(0.7)`

`Z = 0.7`

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