The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 60 and a standard deviation of 8 . Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 44 and 60 ? Do not enter the percent symbol. ans =

Using the empirical rule, we know that for a bell-shaped distribution, about 68% of the data falls within one standard deviation of the mean. In this case, the mean is 60 and the standard deviation is 8. One standard deviation below the mean is 60 - 8 = 52, and two standard deviations below is 60 - 16 = 44. Therefore, the range from 44 to 60 covers a span of two standard deviations below the mean. According to the empirical rule, this means that approximately 95% of the data lies within two standard deviations. Since we are looking for the percentage of requests numbering between 44 and 60, we can estimate it to be half of that 95%, which is around 47.5%. Thus, the answer is approximately: ans = 47.5