Statistics 1342

Question

Midterm examinations were graded for all students currently enrolled in a music appreciation course. The mean exam grade is 85 and the standard deviation is 10. Josie scored a 65 on her midterm examination.

Josie’s exam score is 20 standard deviations to the left of the mean.

Josie’s exam score is 20 standard deviations to the right of the mean.

Josie’s exam score is 2 standard deviations to the left of the mean.

Josie’s exam score is 2 standard deviations to the right of the mean.

Answer 1

As a multiple choice question, we can immediately rule out answers (A) and (B). Remember that 99.7% of all scores will be within 3 standard deviations of the mean. So it is extremely unlikely for a score to be more than 3 standard deviations away from the mean.

Next, we want to check if Josie's score is to the left or right of the mean.

Josie's score is lower than the mean score, so Josie's score is to the left of the mean.

If we actually wanted to check the z-score, use: (x-mu)/sd = (65-85)/10 = -2.