Question

Shalise competed in a jigsaw puzzle competition where participants are timed on how long they take to complete puzzles of various sizes.

Shalise completed a small puzzle in 75 minutes and a large jigsaw puzzle in 140 minutes. For all participants, the distribution of completion
time for the small puzzle was approximately normal with mean 60 minutes and standard deviation 15 minutes. The distribution of completion
time for the large puzzle was approximately normal with mean 180 minutes and standard deviation 40 minutes.
Approximately what percent of the participants had finishing times greater than Shalise's for each puzzle?

Answer 1

Answer B

Explanation:

According to the empirical rule, approximately 68% of the completion times are within one standard deviation of the mean of 60 minutes for the smaller puzzle. By symmetry, 16% of the remaining completion times are less than 45 minutes and 16% of the completion times are greater than 75 minutes. For the large puzzle, the empirical rule guarantees that approximately 68% of the times will be within 1 standard deviation of the mean of 180 minutes. By symmetry, 16% of the remaining times are less than 140 minutes, and 16% of the times are greater than 220 minutes. Therefore 84% of the times will be greater than Shalise’s time of 140 minutes on the large puzzle.

Answer 2

16% on the small puzzle and 84% on the large puzzle.

Explanation: