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 3 inches. using the empirical rule, what percentage of the boys are between 65 and 77 inches tall?

Explanation:

Step1: Calculate z-scores for 65

$z_1 = \frac{65 - 71}{3} = -2$

Step2: Calculate z-scores for 77

$z_2 = \frac{77 - 71}{3} = 2$

Step3: Apply empirical rule

For $z = \pm2$, the empirical rule states the percentage of data within this range is 95%.

Answer:

95%