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 61 and a standard deviation of 9. Using the 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 34 and 61?

Answer 1

Answer: 49.85%

Step-by-step explanation:

Given : 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 ( normal distribution ) and has a mean of 61 and a standard deviation of 9.

i.e.  $\mu=61$ and $\sigma=9$

To find :  The approximate percentage of lightbulb replacement requests numbering between 34 and 61.

i.e. The approximate percentage of lightbulb replacement requests numbering between 34 and $34+3(9)$.

i.e. i.e. The approximate percentage of lightbulb replacement requests numbering between $\mu$ and $\mu+3(\sigma)$. (1)

According to the 68-95-99.7 rule, about 99.7% of the population lies within 3 standard deviations from the mean.

i.e. about 49.85% of the population lies below 3 standard deviations from mean and 49.85% of the population lies above 3 standard deviations from mean.

i.e.,The approximate percentage of lightbulb replacement requests numbering between $\mu$ and $\mu+3(\sigma)$ = 49.85%

⇒ The approximate percentage of lightbulb replacement requests numbering between 34 and 61.= 49.85%