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 month Susan bowls 64 games,what is the probability that her average score in this month is above 227?
A) 0.1093
B) 0.4404
C) 0.5596
D) 0.8907

Question

Quizplus · Accepted Answer

To solve this problem, we need to first calculate the standard error of the mean (SEM) which is given by:
SEM = standard deviation / square root of sample size
SEM = 13 / square root of 64
SEM = 1.625
Next, we need to convert the given average score of 227 into a z-score using the formula:
z = (x - mu) / SEM
z = (227 - 225) / 1.625
z = 1.23
Using a standard normal distribution table, we can find the probability of getting a z-score of 1.23 or higher, which is 0.1093. Therefore, the probability that Susan's average score in this month is above 227 is 0.1093 or approximately 11%. Option A is the best choice.

Susan Has Been on a Bowling Team for 14 Years