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 50 and a standard deviation of 11. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 39 and 50?

Answer 1

34% of lightbulb replacement requests numbering between 39 and 50.

Explanation:

The 68-95-99.7 rule states that, for a normally distributed random variable:

68% are within 1 standard deviation of the mean(34% between one standard deviation below and the mean, 34% between the mean and one standard deviation above the mean).

95% are within 2 standard deviations of the mean.

99.7% are within 3 standard deviations of the mean.

In this problem, we have that:

The distribution of the number of daily requests is bell-shaped and has a mean of 50 and a standard deviation of 11.

Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 39 and 50?

50 is the mean

39 is one standard deviation below the mean.

This means that 34% of lightbulb replacement requests numbering between 39 and 50.