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 53 and a standard deviation of 7. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 53 and 74?

Answer 1

The physical plant at the main campus of a large state university receives daily requests to replace flurocent lightbulbs.

The number of daily requests is bell shaped and has a mean of 53 and a standard deviation of 7.

Now, the 68-95-99.7 rule says that between three standard deviations of the mean, lies 99.7% of all the population.

We have to find the approximate percentage of lightbulb replacement requests numbering between 53 and 74.

Now,

53=53+0*7=mean+0*standard deviation

74=53+3*7=mean+3*standard deviation

Now, this means we have to find the percentage of population between the mean and 3 standard deviations to the right of the mean.

Now, as the normal distribution is symmetric, it is exactly the half of the area between 3 standard deviations of the mean, on both sides.

So, the required percentage is 99.7/2, ie. 49.85%.

The answer is

Approximately 49.85% of lightbulb requests are numbering between 53 and 74.