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(b) Assume that the number of new visitors to a website in one minute is distributed as Poisson variable. The mean number is new visitors to the website is 4.0 per minute. What is the probability that in any given minute Zero new visitors will arrive at the website? (2 marks] (i1) fewer than three new visitors will arrive at the website? (3 marks) (c) Many manufacturing problems involved the matching of machine parts, such as shafts that fit into a valve hole. A particular design requires a shaft with a diameter of 22.000 mm but shafts with diameters between 21.990 mm and 22.010 mm are acceptable. Suppose that the manufacturing process yields shafts with diameters normally distributed, with a mean of 22.022 mm and a standard deviation of 0.005 mm. For this process, what is (i) the probability that a shaft is acceptable? (5 marks) the diameter that will be exceeded by only two percent of the shafts? (5 marks) [Total : 25 Marks]Question 2 (a) Accuracy in taking orders at a drive-through window is important for fast-food chains. Periodically, QSR Magazine published "The Drive-Thru Performance" Study: Order Accuracy" that measures the percentage of orders that are filled correctly. In a recent month, the percentage of orders filled correctly at Wendy's was approximately 86.8%. Suppose that you go to the drive-through window at Wendy's and place an order. Two friends of yours independently place order 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? (6 marks) (ii) What are the mean and standard deviation of the binomial distribution for the number of orders filled correctly? (4 marks)