Disney theme parks are exemplars of operational efficiency. As one example, they hire engineers to monitor the length of lines at rides: if line length exceeds the typical length by too much they will send a diversion--employees dressed as characters, for exampleuto the area to draw some visitors away from the ride. The engineers collect lots of data about line lengths that they consider reasonable, and line length can often be modeled with a normal distribution. Assume that for one ride the mean number of people in the line is 125, with a standard deviation of 5.7 people. The engineers decided that any line length that exceeds 3 standard deviations above the mean is too long and will prompt a diversion to be sent to the area. (This is an example of statistical process control: you'll learn more about this concept in the CSOM core operations course.) a. What's the z-score that corresponds to 3 standard deviations above the mean? b. What's the cutoff number of people in line that will prompt a diversion to be sent to the area? Round up to the nearest whole person. c. How unusual would it be to see a line of 147 people? One way to express "unusualness" is to compute the probability that there are 147 people or even more in line. Enter this as a probability between 0 and 1, to 4 decimal places (enter 0.1234, not 12.3456}. Enter 0 if this number rounds to 0