Question

The physical plant at the main campus of a large state university recieves daily requests to replace florecentlightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 35 and a standarddeviation of 4.Using the 68-95-99.7 rule (also known as the Empirical Rule), what is the approximate percentage of lightbulbreplacement requests numbering between 35 and 43?Do not enter the percent symbol.%

Answer 1

We have to use the empirical rule to find the percentage of requests numbering between 35 and 43.

The number of bulbs requested has a normal distribution with mean of 35 and a standard deviation of 4.

Then, the interval 35 to 43 can be related to the distribution as:

- 35 is the mean so it is 0 standard deviation from the mean.

- 43 is 8 units above the mean, which represents 8/4 = 2 standard deviations.

Then, we can sketch this as:

The empirical rule tells us that 95% of the data is within 2 standard deviations from the mean.

In this case, we represent half that data with the interval [35, 43].

Then, the percentage will be 95/2 = 47.5%.

Answer: 47.5%