Math homework help

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 47 and a standard deviation of 5. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 47 and 62?

Answer 1

47 is right at the midpoint of the distribution. 62 is 3σ (15 = 3*5) above the mean. The tail end greater than 3σ away (or at z=3) will have an area of (1-.997)/2 = .0015. Therefore the area under the curve from 47 to 62 is .5 -.0015.

Or you could take the full area from μ-3σ to μ+3σ and divide by 2: or .997/2