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 is more than 230?
A) 0.0618
B) 0.3520
C) 0.6480
D) 0.9382

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean will also be normally distributed with mean 225 and standard deviation (standard error) of 13/sqrt(16) = 3.25. We calculate the z-score for 230: (230-225)/3.25 = 1.54. Using the standard normal distribution table, the probability of a z-score greater than 1.54 is approximately 0.0618.

Susan Has Been on a Bowling Team for 14 Years