Question

Can someone check over my work I’m not quite sure if I did it right.Jane and John took different exams and wanted to compare their test scores. Use Z-scores to decide who did better by finding who had the higher z score. John got an 83 on test A and Jane got an 80 on test B Test A: Mean = 79, SD= 3.5Test B: Mean = 77, SD= 2.5I got 1.14 for John and 0.857 for Jane, so John had the higher z score.

Answer 1

The z-score can be calculated by the following formula:

$z=\frac{x-m}{\sigma}$

Where m is the mean, σ is the standard deviation and x is the actual score.

By replacing John's result (83) for x, 79 for m and 3.5 for σ, we get:

$z=\frac{83-79}{3.5}=1.14$

Similarly, for Jane's result on test B:

$z=\frac{80-77}{2.5}=1.2$

John's z-score was 1.14 and Jane's z-score was 1.2, then, Jane did better than John