For a customer, the number of books he buys in a bookstore can be treated as a random variable. The probability of not buying any book, buying one book and buying 2 books are 0.05,0.8 and 0.15 for each customer. Suggest there are 400 customers who come to this bookstore today and the number of books purchased by each customer are a sequence of iid random variables. (a) Find the probability that the bookstore could sell more than 450 books (the sum of all customers buying) today.(Hint: use central limit theorem)

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For a customer, the number of books he buys in a bookstore can be treated as a random variable. The
probability of not buying any book, buying one book and buying 2 books are 0.05,0.8 and 0.15 for each
customer. Suggest there are 400 customers who come to this bookstore today and the number of books
purchased by each customer are a sequence of iid random variables.
(a) Find the probability that the bookstore could sell more than 450 books (the sum of all customers buying)
today.(Hint: use central limit theorem)
Transcribed Image Text:For a customer, the number of books he buys in a bookstore can be treated as a random variable. The probability of not buying any book, buying one book and buying 2 books are 0.05,0.8 and 0.15 for each customer. Suggest there are 400 customers who come to this bookstore today and the number of books purchased by each customer are a sequence of iid random variables. (a) Find the probability that the bookstore could sell more than 450 books (the sum of all customers buying) today.(Hint: use central limit theorem)
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According to the provided data, the mean and standard deviation for each customer is,

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