Question

he 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 59 and a standard deviation of 7. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 52 and 59?

Answer 1

Answer: 34%

Explanation:

Given : The distribution of the number of daily requests is bell-shaped and has a mean of 59 and a standard deviation of 7.

i.e.
`\mu=59` and
`\sigma=7`

According to the 68-95-99.7 rule, about 68% of the population lies in one standard deviation from the mean.

About 34% of the population lies one standard deviation above the mean and About 34% of the population lies one standard deviation below the mean.

For the given situation, 34% of lightbulb replacement requests lies one standard deviation below the mean .

i.e.About 34% of lightbulb replacement requests lies between
`\mu-\sigma` and
`\mu` .

i.e. About 34% of lightbulb replacement requests lies between
`59-7` and
`59` .

i.e. About 34% of lightbulb replacement requests lies between
`52` and
`59` .

Hence, the approximate percentage of lightbulb replacement requests numbering between 52 and 59 = 34%