Question

Heights of men on a basketball team have a bell shaped distribution with a mean of 173 cm and a standard deviation of 8 cm using the empirical rule what is the approximate percentage of the men between the following

a. 165 cm and 181 cm
b. 149 cm and 197cm

Answer 1

a. 68%

b. 99.7%

Explanation:

Bell-shaped distribution means Normal distribution.

For finding the percentage first we have to calculate the value of:
`(x-\bar x)/(\sigma)`

If its value is ±1, then using empirical formula percentage = 68%

If its value is ±2, then using empirical formula percentage = 95%

and, If its value is ±3, then using empirical formula percentage = 99.7%

a.
`(165 - 173)/(8) = -1 \ \ and \ \ (181 - 173)/(8) = 1`

Thus, 68% of data lie within 1 standard deviation of the mean.

b.
`(149 - 173)/(8) = -3 \ \ and \ \ (197 - 173)/(8) = 3`

Thus, 99.7% of data lie within 3 standard deviation of the mean.

Answer 2

I have a similar problem here with a slightly different given.

Heights of men on a baseball team have a bell shaped distrubtion with a mean of 172cm and a standard deviation of 7cm. Using that is the empirical rule, what is the approximate percentage of the men between the following values?
a) 165 cm and 179cm
b) 151cm and 193cm

The solution is:

a. (165-172)/7 = -1, (179-172)/7 = 1, % by empirical rule = 68%

b. (151-172)/7 = -3, (193-172)/7 = 3, % by empirical rule = 99.7%

I hope that by examining the solution for this problem, it could help you answer your problem on your own.