Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below:

- Rebecca got a score of 97.8; this version has a mean of 72.3 and a standard deviation of 15.
- Frankie got a score of 272; this version has a mean of 242 and a standard deviation of 20.
- Kiersten got a score of 7.66; this version has a mean of 6.9 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?

Kiersten, with a z-score of 1.90, outperformed the others. She should be offered the job as she had the highest relative score on her version of the test.

To determine which applicant should be offered the job based on their aptitude test scores, we can use a statistical measure called z-scores. The z-score tells us how many standard deviations a particular score is from the mean. The higher the z-score, the better the applicant performed compared to others who took the test.

Here's how you can calculate the z-scores for each applicant:

1. For Rebecca:

Z-Rebecca = (Score-Rebecca - Mean-Rebecca) / Standard Deviation-Rebecca

Z-Rebecca = (97.8 - 72.3) / 15 = 1.72

2. For Frankie:

Z-Frankie = (Score-Frankie - Mean-Frankie) / Standard Deviation-Frankie

Z-Frankie = (272 - 242) / 20 = 1.50

3. For Kiersten:

Z-Kiersten = (Score-Kiersten - Mean-Kiersten) / Standard Deviation-Kiersten

Z-Kiersten = (7.66 - 6.9) / 0.4 = 1.90

Now, we have calculated the z-scores for each applicant. A higher z-score indicates a better performance relative to the mean of their respective test versions.

In this case, Kiersten has the highest z-score of 1.90, indicating that she performed the best relative to the other test takers in her version of the test. Therefore, based on the aptitude test scores, Kiersten should be offered the job.

To learn more about z-score here

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