6. let x1, x2,... xn be a sequence of independent bernoulli variates such that px= 1) =p, pcx; = 0) = q, p +q=1. let x = (22xi)/n, 1 sišn. verify central limit

6. Let X1, X2,... Xn be a sequence of independent Bernoulli variates such that PX= 1) =p, PCX; = 0) = q, p +q=1. Let X = (22Xi)/n, 1 sišn. Verify Central Limit Theorem by showing that X tends to be Normal as n > co. A customer care center is operating in such a manner that the number of customers attended on a particular day is a random variable with mean of 250 persons and a standard deviation of 20 persons. Use the Central Limit Theorem or otherwise, find the probability that the average (mean) number of customers attended in a random sample of 45 days is at least 255?

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