Question

The physical plant at the main campus of a large state university receives daily requests to replace florescent light-bulbs. The distribution of the number of daily requests is Normally distributed with a mean of 62 and a standard deviation of 8. Using the Empirical Rule, what is the approximate percentage of light-bulb replacement requests numbering between 54 and 62? Do not enter the percent symbol. ans = %

Answer 1

Given:

Let X be a random variable which denotes the number of daily requests to replace florescent light-bulbs

Mean, = 62

Standard deviation, = 8

To find P(54 <= X <= 62) * 100%

54 = 62 - 8 =

Thus, P(54 <= X <= 62) = P( <= X <= )

From Empirical rule, 68% of the values lies within one standard deviation(both left and right) of the mean

Thus, 68/2 = 34% of the values lies between mean and one standard deviation

The answer is 34 %