Question

In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 2.5 inches. Using the empirical rule, determine the interval of heights that represents the middle 95% of male heights from this school.

Answer 1

Answer: the interval of heights that represents the middle 95% of male heights from this school is between 66 inches and 76 inches.

Step-by-step explanation:

Let x be a random variable representing the heights of males from this school. With the mean and standard deviation given, then the Empirical Rule says the that

1) About 68% of the x values lie between 1 standard deviation below and above the mean.

2) About 95% of the x values lie between 2 standard deviations below and above the mean.

3) About 99.7% of the x values lie between 3 standard deviations below and above the mean.

From the information given,

mean = 71 inches

Standard deviation = 2.5 inches

We want to determine where 95% of x values lies. This is 2 standard deviations from the mean Therefore,

2 standard deviations = 2 × 2.5 = 5 inches

The heights are

71 - 5 = 66 inches and

71 + 5 = 76 inches