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 55 and 85 inches tall?
According to the empirical rule (also known as the 68-95-99.7 rule), approximately:
- 68% of the data falls within one standard deviation of the mean
- 95% of the data falls within two standard deviations of the mean
- 99.7% of the data falls within three standard deviations of the mean
Since the mean height is 70 inches and the standard deviation is 5 inches, one standard deviation above and below the mean would be 70 + 5 = 75 inches and 70 - 5 = 65 inches, respectively.
Therefore, approximately 68% of the boys are between 65 and 75 inches tall.
To find the percentage of boys between 55 and 85 inches tall (which is within two standard deviations of the mean), we can add in the extra 27% of data that falls within two standard deviations of the mean. So, 68% + 27% = 95%.
Therefore, approximately 95% of the boys are between 55 and 85 inches tall.