Susan has been on a bowling team for 14 years.After examining all of her scores over that period of time,she finds that they follow a normal distribution.Her average score is 225,with a standard deviation of 13.If during a typical week Susan bowls 16 games,what is the probability that her average score for the week is between 220 and 228?
A) 0.0618
B) 0.2390
C) 0.7594
D) 0.8212

Question

Quizplus · Accepted Answer

First, we need to find the z-scores for both the lower and upper bounds:

Lower z-score = (220 - 225) / (13 / sqrt(16)) = -2.06
Upper z-score = (228 - 225) / (13 / sqrt(16)) = 1.23

Next, we need to find the area between these two z-scores using a standard normal distribution table or calculator. The area between -2.06 and 1.23 is approximately 0.7594.

Therefore, the probability that Susan's average score for the week is between 220 and 228 is 0.7594 or approximately 76%.

Susan Has Been on a Bowling Team for 14 Years