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) 0.1092
B) 0.4404
C) 0.5596
D) 0.8907

Question

Quizplus · Accepted Answer

First, we need to find the distribution of Susan's average score in a month. Since her scores follow a normal distribution, the average score in a month will also follow a normal distribution with a mean of 225 and a standard deviation of $\frac{13}{\sqrt{64}} = 1.625$.

Next, we need to find the probability that her average score in a month is above 227. We can calculate this using the z-score formula:

$$z=\frac{x-\mu}{\sigma}=\frac{227-225}{1.625}=1.23$$

Using a standard normal distribution table or calculator, we can find that the probability of a z-score being greater than 1.23 is 0.1092.

Therefore, the probability that Susan's average score in a month is above 227 is 0.1092 or approximately 11%. The best choice is A.

Susan Has Been on a Bowling Team for 14 Years