Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.
-If a regulation basketball is randomly selected, what is the probability that it will weigh between 20.5 and 23.5 ounces? Round to the nearest thousandth.
A)0.134
B)0.704
C)0.866
D)0.267

Question

Quizplus · Accepted Answer

To find the probability that a basketball weighs between 20.5 and 23.5 ounces, we calculate the z-scores for 20.5 and 23.5 using the mean of 22.0 and standard deviation of 1.0. The z-score for 20.5 is -1.5 and for 23.5 is 1.5. Using the standard normal distribution table, the probability for z = -1.5 is 0.0668 and for z = 1.5 is 0.9332. The probability of the basketball weighing between these values is 0.9332 - 0.0668 = 0.866.

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