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 48 and a standard deviation of 5. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 33 and 48?

Answer 1

Mean = 48

65-95-99.7 rule tells us:

65% of the data falls within 1 st. dev of the mean (both sides equally)

95% of the data falls within 2 st. dev of the mean (both sides equally)

99.7% of the data falls within 3 st. dev of the mean (both sides equally)

We want to find between 33 and 48.

48 is the mean, so we need to find within one side (left) of the mean.

48 - 33 = 15 (that is 3 standard deviation, 5 + 5 + 5 = 15)

This is basically 1 side of the curve.

3 standard deviation means 99.7%, but since this is HALF of that total, we have:

99.7%/2 = 49.85%

Note: