Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Emilio got a score of 76; this version has a mean of 70.6 and a standard deviation of 9. Alissa got a score of 298.8; this version has a mean of 282 and a standard deviation of 24. Tobias got a score of 8.04; this version has a mean of 7.2 and a standard deviation of 0.4.

Required:
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?

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For Emilio

Emilio got a score of 76; this version has a mean of 70.6 and a standard deviation of 9.

z = (x-μ)/σ

z = 76 - 70.6/9

z = 0.6

For Alissa

Alissa got a score of 298.8; this version has a mean of 282 and a standard deviation of 24.

z = (x-μ)/σ

z = 298.8 - 282/24

z = 0.7

For Tobias

Tobias got a score of 8.04; this version has a mean of 7.2 and a standard deviation of 0.4.

z = (x-μ)/σ

z = 8.04 - 7.2/0.4

z = 2.1

Looking at the calculated z score above, we can see that Tobias did better on his aptitude test because he had a higher z score compared to Emilio and Alissa.