When a pizza restaurant's delivery process is operating effectively, pizzas are delivered in an average of 45 minutes with a standard deviation of 6 minutes. To monitor its delivery process, the restaurant randomly selects five pizzas each night and records their delivery times.
a. For the sake of argument, assume that the population of all delivery times on a given evening is normally distributed with a mean of m = 45 minutes and a standard deviation of s = 6 minutes. (That is, we assume that the delivery process is operating effectively.) Find the mean and the standard deviation of the population of all possible sample means, and calculate an interval containing 99.73 percent of all possible sample means.
b. Suppose that the mean of the five sampled delivery times on a particular evening is x = 55 minutes. Using the interval that you calculated in a, what would you conclude about whether the restaurant's delivery process is operating effectively? Why?