The statistics-conscious store manager at Marketview records the number of customers who walk through the door each day. Years of records show the mean number of customers per day to be 586 with a standard deviation of 165. Assume the number of customers is normally distributed.
a. What is the probability that on any given day, the number of customers exceeds 1000?
b. If 20 days are randomly selected, what is the probability that the mean of this sample is less than 550?
c. The assumption of normality allowed you to calculate the probabilities; however, this may not be a reasonable assumption. Explain why and how that affects the probabilities found in parts a and b.