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 53 and a standard deviation of 8 . Using the empirical rule, what is the approximate percentage of lightbulb replacement requests numbering between 37 and 53 ? Do not enter the percent symbol. ans =

Using the empirical rule, which states that in a normal distribution, about 68% of the data falls within one standard deviation of the mean, we can analyze the data. Since the mean is 53 and the standard deviation is 8, one standard deviation below the mean is 53 - 8 = 45. The range of 37 to 53 can be evaluated as follows: - 37 is two standard deviations below the mean (53 - 16 = 37). - Therefore, we need to account for data between the mean (53) and two standard deviations below it (37). According to the empirical rule: - About 95% of the values lie within two standard deviations of the mean (between 37 and 69). Since 50% of the data is below the mean and we just want the portion below 53, we will take half of the remaining percentage of data within those two standard deviations. So, from 37 to 53, we find: 95% / 2 = 47.5% below the mean + 50% below the mean = 47.5% from the lower side of 37 to 53. Thus, the approximate percentage of lightbulb replacement requests numbering between 37 and 53 is approximately 47.5. The answer is: 47.5