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?

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JeanaShupp JeanaShupp · Answer 1 · 2019-12-05T06:59:11+01:00

Answer: 34%

Step-by-step 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. [tex]\mu=59[/tex] and [tex]\sigma=7[/tex]

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 [tex]\mu-\sigma[/tex] and [tex]\mu[/tex] .

i.e. About 34% of lightbulb replacement requests lies between [tex]59-7[/tex] and [tex]59[/tex] .

i.e. About 34% of lightbulb replacement requests lies between [tex]52[/tex] and [tex]59[/tex] .

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