Question

In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 3 inches. Using the empirical rule, determine the interval of heights that represents the middle 95% of male heights from this school.

Answer 1

The interval of heights that represents the middle 95% of male heights from this all boys school is between 63 inches and 75 inches.

Step-by-step explanation:

To determine the interval of heights that represents the middle 95% of male heights from this all boys school, we can use the empirical rule. According to the empirical rule, for a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.

In this case, the mean height is 69 inches and the standard deviation is 3 inches. So, within 2 standard deviations of the mean, we expect to find the middle 95% of the data. Calculating the interval:

Lower bound = mean - 2 * standard deviation = 69 - 2 * 3 = 63 inches

Upper bound = mean + 2 * standard deviation = 69 + 2 * 3 = 75 inches

Therefore, the interval of heights that represents the middle 95% of male heights from this all boys school is between 63 inches and 75 inches.

Answer 2

Answer: 65.5, 72.5

Step-by-step explanation: