In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 5 inches. Using the empirical rule, what percentage of the boys are between 60 and 80 inches tall?
Answer
\(\boxed{95\%}\) of the boys are between \(60\) and \(80\) inches tall
Step 1 ：Given a normal distribution with mean \(\mu = 70\) inches and standard deviation \(\sigma = 5\) inches
Step 2 ：Find the percentage of boys with heights between \(60\) and \(80\) inches
Step 3 ：Using the empirical rule, we know that approximately \(95\%\) of the data falls within two standard deviations of the mean
Step 4 ：Since \(60\) inches is \(2\) standard deviations below the mean and \(80\) inches is \(2\) standard deviations above the mean, we can conclude that
Step 5 ：\(\boxed{95\%}\) of the boys are between \(60\) and \(80\) inches tall
