Question

Question 10The physical plant at the main campus of a large state university recieves daily requests to replace florecentlightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 56 and a standarddeviation of 11. Using the Empirical Rule rule, what is the approximate percentage of lightbulb replacementrequests numbering between 56 and 89?Do not enter the percent symbol.ans =%

Answer 1

We know that the empirical rule states that 99.7% of the area is in the interval:

$(\mu-3\sigma,\mu+3\sigma)$

In this case we notice that we are looking at the interval (56,89) in a normal distribution with mean 56 and standard deviation 11, which means that we area in the interval:

$(\mu,\mu+3\sigma)$

which means that we have half the area of the interval mentioned before. Therefore, the approximate percentage between 56 and 89 is 49.85%