Question

determine whether the statement makes sense or does not make sense, and explain your reasoning. the heights of the men on our college basketball team are normally distributed with a mean of 6 feet 3 inches and a standard deviation of 1 foot 2 inches. choose the correct answer below. a. no, this does not make sense because this would mean that approximately 68% of the players on the team would be between 5 feet 8 inches and 6 feet 10 inches and that approximately 95% of the players on the team would be between 5 feet 1 inch and 7 feet 5 inches. b. no, this does not make sense because this would mean that approximately 95% of the players on the team would be between 5 feet 1 inch and 7 feet 5 inches and that approximately 99.7% of the players on the team would be between 3 feet 11 inches and 8 feet 7 inches. c. yes, it makes sense. d. no, this does not make sense because this would mean that approximately 68% of the players on the team would be between 5 feet 1 inch and 7 feet 5 inches and that approximately 95% of the players on the team would be between 3 feet 11 inches and 8 feet 7 inches.

Explanation:

Step1: Recall normal - distribution properties

In a normal distribution, about 68% of the data lies within 1 standard - deviation of the mean, about 95% lies within 2 standard - deviations of the mean, and about 99.7% lies within 3 standard - deviations of the mean.
The mean height is 6 feet 3 inches = 75 inches (since 1 foot = 12 inches, 6×12 + 3=75 inches), and the standard deviation is 1 foot 2 inches = 14 inches.

Step2: Calculate 1 - standard - deviation range

The range within 1 standard - deviation of the mean: Lower limit = 75−14 = 61 inches = 5 feet 1 inch, Upper limit = 75 + 14 = 89 inches = 7 feet 5 inches.

Step3: Calculate 2 - standard - deviation range

The range within 2 standard - deviations of the mean: Lower limit = 75−2×14=75 - 28 = 47 inches = 3 feet 11 inches, Upper limit = 75 + 2×14=75 + 28 = 103 inches = 8 feet 7 inches.
A range of 3 feet 11 inches to 8 feet 7 inches for 95% of the players' heights is not reasonable for a college basketball team.

Answer:

B. No, this does not make sense because this would mean that approximately 95% of the players on the team would be between 5 feet 1 inch and 7 feet 5 inches and that approximately 99.7% of the players on the team would be between 3 feet 11 inches and 8 feet 7 inches.