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 57 and a standard deviation of 11. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 57 and 79?

Answer 1

According to 68-95-99.7 rule, 68%, 95% and 99.7% of data values lie within 1, 2 and 3 standard deviations of mean.

Here, mean = 57

Standard deviation = 11

The value 57 is the mean and hence, 50% of values are above mean

57 + 2 x 11 = 79

79 is 2 standard deviations above mean

Of the 95% that lies within 2 standard deviations of mean, half lies above mean and half lies below mean.

Therefore, approximate percentage of lightbulb replacement requests numbering between 57 and 79 = 95/2

= 47.5%