math: statistics

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 49 and a standard deviation of 7. Using the 68-95-99.7 (Empirical) Rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 49?

The approximate percentage of lightbulb replacement requests numbering between 42 and 49 is  %. (Do not enter the percent symbol.)

Answer 1

Hi Ashlee,

Notice that 42 is one standard deviation below the mean (49). The Empirical Rule states that about 68% of the data in a normal distribution will be between one standard deviation below and one standard deviation above the mean.

Since the normal distribution is symmetric, we can simply cut that in half to find the approximate percentage of data that is between a boundary one standard deviation below the mean and the mean itself:

68/2 = 34

So the answer is 34%

Does that make sense?