The distribution of the number of requests is bell-shaped and has a mean of 54 and a standard deviation of 11.

Question

The physical plant at the main campus of a large state school receives daily requests to to replace lightbulbs. The distribution of the number of requests is bell-shaped and has a mean of 54 and a standard deviation of 11. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 54 and 87?

Answer 1

How many standard deviations are there between the mean (54) and the upper limit of the range (87)?

Compute: 87 - 54 = 33

standard deviation = 11, so there are 33/11 = 3 standard deviations between the mean and upper limit.

Per the empirical rule, there is 49.9% of the requests within 3 standard deviations above the mean.