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. \[ \text { ans }=\square \% \] Check Answer
Solution
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 \( \boxed{34\%} \).
