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 2.5 inches. using the empirical rule, determine the interval of heights that represents the middle 99.7% of male heights from this school. answer attempt 1 out of 3

Explanation:

Step1: Recall the empirical rule

The empirical rule for a normal - distribution states that approximately 99.7% of the data lies within 3 standard deviations of the mean.

Step2: Calculate the lower bound

The lower bound is given by the formula $\mu - 3\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. Here, $\mu = 69$ inches and $\sigma=2.5$ inches. So, the lower bound is $69 - 3\times2.5=69 - 7.5 = 61.5$ inches.

Step3: Calculate the upper bound

The upper bound is given by the formula $\mu + 3\sigma$. So, the upper bound is $69+3\times2.5 = 69 + 7.5=76.5$ inches.

Answer:

The interval is $[61.5,76.5]$ inches.