2. Answer questions in Problem 11, if the demand for mugs follows a Normal distribution with mean 160 and standard deviation 50. 11- A bookstore is planning to order mugs that are designed for Valentines day. The store buys a mug for $7.50 and sells it for $8.99. Because the store asked the manufacturer of the mug to print the bookstores logo at the bottom of the mugs, the store needs to place its order 6 weeks in advance. The bookstore, therefore, has decided to place only one order 2 months before Valentines day. All the mugs that are not sold by Valentines day will be sold at the price of $3.99 to a discount store. The demand for the mugs is believed to follow a Poisson distribution with mean 160. The store manager has decided to order 180 mugs. a. How many mugs should the manager order to maximize their expected profit? b. What is the probability of not having shortage of mugs, if the manager orders optimally to maximize expected profit? e. What fraction of customers will face shortage if the manager orders optimally?