The physical plant at the main campus of a large state university receives daily requests to replace florescent light-bulbs.

Question

The distribution of the number of daily requests is bell-shaped and has a mean of 54 and a standard deviation of 6. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 51 and 56?

Answer 1

Per the empirical rule 34% of the data is within one standard deviation to the left of the mean. 51 is 1/2 standard deviation to the left of 54, so 34%/2 = 17% of the data is between 51 and 54.

34% of the data is within one standard deviation to the right of the mean. 56 is 1/3 standard deviation to the right of 54, so 34%/3 = 11.33% of the data is between 54 and 56.

Adding the percentages 17% + 11.33% = 28.33% of the data is between 51 and 56.