5.5

Accuracy in taking orders at a drive-through window is important for fast-food chains. Periodically, QSR Magazine publishes the results of a survey that measures accuracy, defined as the percentage of orders that are filled correctly. In a recent year, the percentage of orders filled correctly at Wendy's was approximately 87.6% (bit.lyfNELUyi). Suppose that you go to the drive-through window at Wendy's and place an order. Two friends of yours independently place orders at the drive-through window at the same Wendy's. What are the probabilities that all three, that none of the three, and that at least two of the three orders will be filled correctly? What are the mean and standard deviation of the binomial distribution for the number of orders filled correctly?