High Achievers
Jack and Jill are top students in their grade level, and they both love statistics. They are in separate statistics classes, but they take the same exams throughout the school year.
On a recent exam, Jack scored 98 out of 100 while Jill scored 97 out of 100. However, we know that in Jack's class the mean score was 80 with a standard deviation of 5, while in Jill's class the mean score was 82 with a standard deviation of 4. The scores in each class are normally distributed.
Relative to each one's class, which student did better on the exam?
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1 solution
To find how each student did relative to their class, we calculate their standard z-scores. For Jack,
z Jack = σ x − μ = 5 9 8 − 8 0 = 3 . 6 .
For Jill,
z Jill = σ x − μ = 4 9 7 − 8 2 = 3 . 7 5 .
Since Jill's z-score is greater than Jack's, we conclude Jill did better on the exam relative to her class.