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 60 and a standard deviation of 11. Using the Empirical Rule rule, what is the approximate percentage of lightbulb replacement requests numbering between 60 and 71?

Answer 1

Answer: 34%

Step-by-step explanation:

According to the Empirical rule,

About 68% of the population lies with in one standard deviation from the mean.

i.e. About  34% of the population lies above one standard deviation from the mean .

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

Given : The distribution of the number of daily requests is bell-shaped ( i.e. Normally distribution) and has a mean of 60 and a standard deviation of 11.

i.e. $\mu=60\ \ \sigma=11$

Using the Empirical Rule rule,  34% of the population of lightbulb replacement requests lies above one standard deviation from the mean .

i.e. About 34% of the population of lightbulb replacement requests lies between $\mu$ and $\mu+\sigma$

i.e. About   34% of the population of lightbulb replacement requests lies between $60$ and $60+11$

i.e. About  34% of the population of lightbulb replacement requests lies between 60 and 71

Hence, the approximate percentage of lightbulb replacement requests numbering between 60 and 71 = 34%