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(4 pt) Let X1, X2, Xn be nindependently and identically distributed random variables with mean p, and variance 0? . While we have learned in class that by the Central Limit Theorem (CLT), the average of X1, X2, and Xn approximately follows a normal distribution when n is relatively large. It is known by the CLT that the sum, \" ' u . . o T = Emir, also approXImately follows a normal distribution With mean Hi! and variance \"0,2 Now let Xdenote the number of tickets a person buys at a summer concert. From the past experience, it is known that on average, each person buys 2.5 tickets (Le, a person may buyr multiple tickets for his/her friends or family] and the variance is 4. Imagine that a few hours before the concert, there are 100 (independent) people standing in line to purchase tickets. a. If only 250 tickets remain, what is the probability that all the 100 concertgoers will be able to purchase the tickets they desire? (2 pt] b. To ensure that the probability of running out of tickets for the remaining 100 concertgoers waiting in line is no more than 5%, at least how many additional tickets (i.e., in addition to the 250 tickets] should the concert organizer have? {2 pt)