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 bell-shaped and has a mean of 37 and a standard deviation of 8. Using the empirical (68-95-99.7) rule, what is the approximate percentage of light bulb replacement requests numbering between 37 and 61

Answer 1

49.85% of light bulb replacement requests numbering between 37 and 61

Explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 37, Standard deviation = 8

Using the empirical (68-95-99.7) rule, what is the approximate percentage of light bulb replacement requests numbering between 37 and 61

37 is the mean

61 = 37 + 3*8, so 61 is three standard deviations above the mean

The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.

By the Empirical Rule, of the 50% of the measures that are above the mean, 99.7% will be between the mean of 37 and three standard deviations above the mean, which is 61. So, this percentage is:

0.5*0.997 = 0.4985 = 49.85%