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.

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

8.75

how-to:

first, we need to find what we have to work with.

since i know that we have 7 (years) and 0.8 (inches), we can use these to solve and find the equation!

secondly, what you want to do, is see that we need to know how much growth out of the 0.8 inches he got in only 1 year, instead of 7 years.

let's try to divide.

7 ÷ 0.8 = 8.75