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 3 inches. Using the empirical rule, what percentage of the boys are between 62 and 74 inches tall?
According to the empirical rule, approximately:
- 68% of the boys will be within 1 standard deviation of the mean, which in this case is between 65 inches (68 - 3) and 71 inches (68 + 3).
- 95% of the boys will be within 2 standard deviations of the mean, which in this case is between 62 inches (68 - 2*3) and 74 inches (68 + 2*3).
Therefore, the percentage of boys between 62 and 74 inches tall is approximately 95%.