Application of standard deviation

Question

1. The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 63 and a standard deviation of 3. Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 63 and 72?

Answer 1

The "empirical rule" is the idea that in a normal distribution (bell-shaped): 68% of all values lie within one standard deviation of the mean, 95% of all values lie within 2 standard deviations of the mean, and 99.7% of all values lie within 3 standard deviations of the mean.

This implies that approximately 99.7% of all daily lightbulb replacement requests number between 3 standard deviations of the mean, i.e. between 63 - 3*3 = 54 and 63 + 3*3 = 72.

Owing to the symmetry of normal distributions, we can say that approximately 99.7%/2 = 49.85% of all daily lightbulb replacement requests number between 63 and 72 (while 49.85% lie between 54 and 63).

Hope this helps! Please let me know of any questions.

Answer 2