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. Refer to Exhibit 7-3.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

We need to find the probability that Susan's average score is more than 230 in a typical week of 16 games.

First, we need to find the standard error of the mean (SEM):

SEM = standard deviation / square root of sample size
SEM = 13 / √16
SEM = 3.25

Next, we need to calculate the z-score for an average score of 230:

z = (x̄ - μ) / SEM
z = (230 - 225) / 3.25
z = 1.54

Using a z-table, we find that the probability of getting a z-score greater than 1.54 is 0.0618. Therefore, the probability that Susan's average score is more than 230 is 0.0618 or approximately 6.18%.

So, the best choice is A.

Susan Has Been on a Bowling Team for 14 Years