What is the approximate percentage of light-bulb replacement requests numbering between 45 and 65?

Question

The physical plant at the main campus of a large state university receives daily requests to replace florescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 65 and a standard deviation of 10. Using the 68-95-99.7 (Empirical) Rule, what is the approximate percentage of lightbulb replacement requests numbering between 45 and 65?

Answer 1

45 is two standard deviations below the mean, so we need to determine from the Empirical Rule the percentage of area under the normal curve between the mean and the mean - two standard deviations.

Between the mean - 2 standard deviations and the mean - 1 standard deviation is 13.5% of the area

Between the mean - 1 standard deviation and the mean is 34 % of the area

In total there is 13.5% + 34% = 47.5% of the area between the mean and mean - two standard deviations