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) 0.7600
D) 0.8212

Question

Quizplus · Accepted Answer

The average score for a week of bowling 16 games is equal to the average score for one game multiplied by 16, which is 225 * 16 = 3600.

The standard deviation for the average score for a week of bowling 16 games is equal to the standard deviation for one game divided by the square root of the number of games, which is 13 / √16 = 3.25.

We can use the z-score formula to find the probability that her average score for the week is between 220 and 228:

z1 = (220 - 3600) / 3.25 = -1276.92
z2 = (228 - 3600) / 3.25 = -1243.08

Using a standard normal distribution table or calculator, we can find the probability that z is between -1276.92 and -1243.08, which is approximately 0.7600.

Therefore, the probability that Susan's average score for the week is between 220 and 228 is 0.7600 or 76.00%, which corresponds to choice C.

Susan Has Been on a Bowling Team for 14 Years