Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below
. Nico got a score of 88.3; this version has a mean of 66.2 and a standard deviation of 13. Justin got a score of 226.2; this version has a mean of 216 and a standard deviation of 17. Tera got a score of 7.97; this version has a mean of 7.2 and a standard deviation of 0.7. 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?
In order to compare who had the best performance on the aptitude test, we can use Z score. Z score indicates how many standard deviation a result is over the mean. For this case the higher the result is, the best is the performance on the aptitude test.
Z score is expressed with the following formula:
Z=(X-μ)/σ
Where:
X is the test score
µ is the mean
σ is the standard deviation
Replacing in the formula we obtained
For Nico:
X = 88.3
µ = 66.2
σ = 13
Z=(88.3-66.2)/13=1.7
For Justin:
X = 226.2
µ = 216
σ = 17
Z=(226.2-216)/17=0.6
For Tera:
X = 7.97
µ = 7.2
σ = 0.7
Z=(7.97-7.2)/0.7=1.1
Nico had the higher Z score which means he had the better performance on the test and he should be offered the job.
This can be solved by imagining the triangle formed by the building and its shadow. The hypotenuse of the triangle, the distance from the tip of the building to the tip of the shadow, is 34 meters, and one of the legs is 29 meters. Therefore, we can use the Pythagorean theorem to find that the third side is . Hope this helps!
