Question

question
watch video show examples
in an all boys school, the heights of the student body are normally distributed with a
mean of 68 inches and a standard deviation of 2.5 inches. using the empirical rule,
what percentage of the boys are between 65.5 and 70.5 inches tall?
answer attempt 1 out of 2

Explanation:

Step1: Calculate the number of standard deviations from the mean

For \(x_1 = 65.5\): \(z_1=\frac{65.5 - 68}{2.5}=\frac{- 2.5}{2.5}=-1\)
For \(x_2 = 70.5\): \(z_2=\frac{70.5 - 68}{2.5}=\frac{2.5}{2.5}=1\)

Step2: Apply the empirical rule

The empirical rule states that for a normal distribution, approximately \(68\%\) of the data lies within \(z=-1\) and \(z = 1\) (i.e., within \(1\) standard deviation of the mean)

Answer:

\(68\%\)