Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 26 and 41?

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 41 and a standard deviation of 5. 

Answer 1

The 68-95-99.7 rule states that 68% of the area underneath the curve is found within 1 standard deviation of the mean, 95% is within 2 standard deviations, and 99.7% is within 3 standard deviations. Requests between 26 and 41 would range between (41-26)/15 = 3 standard deviations below the mean, and 41 = the mean (the bottom half of the 3-standard deviation range). The area covered is thus 99.7%/2 = 49.85%.

Answer 2

26 is 3 standard deviations below 41, which is 49.9% of the area under the normal curve.