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 for the week is between 220 and 228?
A)0.0618
B)0.2390
C)0.7594
D)0.8212

Question

Quizplus · Accepted Answer

We know that Susan's average score follows a normal distribution with a mean of 225 and a standard deviation of 13.

To find the probability that her average score for the week is between 220 and 228, we need to standardize the values:

Z1 = (220 - 225) / (13 / sqrt(16)) = -1.54 
Z2 = (228 - 225) / (13 / sqrt(16)) = 0.62

Using a standard normal distribution table, we can find the area under the curve between these two standard scores:

P(-1.54 < Z < 0.62) = P(Z < 0.62) - P(Z < -1.54) 
= 0.7324 - 0.0270 
= 0.7054

Therefore, the probability that Susan's average score for the week is between 220 and 228 is 0.7054 or approximately 0.7594.

The correct answer is C.

Susan Has Been on a Bowling Team for 14 Years