Problem

The physical plant at the main campus of a large state university recieves daily requests to replace florecent Iightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 43 and a standard deviation of 4. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 35 and 43 ?
(Round percent number to 2 decimal places.)

Do not enter the percent symbol.
\[
\text { ans }=\square \%
\]
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Answer

So, the approximate percentage of lightbulb replacement requests numbering between 35 and 43 is \( \boxed{34\%} \).

Steps

Step 1 :The physical plant at the main campus of a large state university receives daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 43 and a standard deviation of 4.

Step 2 :We are asked to find the approximate percentage of lightbulb replacement requests numbering between 35 and 43.

Step 3 :Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Since 43 - 35 = 8, which is two standard deviations away from the mean, we only need half of the 68%, which is 34%.

Step 4 :So, the approximate percentage of lightbulb replacement requests numbering between 35 and 43 is \( \boxed{34\%} \).

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