How would I do this

Question

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 60 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 57 and 60?

Answer 1

See the following graph if you are unsure about the "empirical rule"--which has a component that states about 68% of the data for a bell shaped curve lies within one standard deviation of the mean.

desmos.com/calculator/9x5yyebvzl

In this problem the mean is 60 with a standard deviation of 3. The data within one standard deviation would be between 57 and 63 (within 3 of the mean in either direction). But you are asked only about the interval from 57 to 60. Since the curve is bell shaped (symmetric about the mean) you are only considering 1/2 of that 68%.