Shipments of television set that arrive at a factory have varying levels of qual

Question

Shipments of television set that arrive at a factory have varying levels of quality. In order to decide whether to accept a particular shipment, inspectors randomly select a sample of 10 television sets and test them; if no more than one television set in the sample is defective, the shipment is accepted. Suppose a very large shipment arrives in which 2% of the television sets are defective. Let X be a random variable representing the number of defective television set in the random sample of 10. Show all work by hand. a.What is the probability that this shipment is accepted? (Use a table or the formula). b.What is the expected value of the number of defective television set in the sample? c.Fill in the blanks in the following sentence: According to the Law of Large Numbers, if we have obtained many different simple random samples of size ______ from this shipment, the average number of defective television set per sample would be approximately _______ I ask this question twice please could you explain in details P(X<=1) = P(X=0) + P(X=1) = 0.8171 +0.1667 = 0.9838 how should I get the amount 0.8171 and 0.1667 from above. Thank you.

Explanation / Answer

p = 0.02

n = 10

This is a binomial distribution

P(X = x) = 10Cx * 0.02x * (1 - 0.02)10-x

P(X < 1) = P(X = 0) + P(X = 1)

              = 10C0 * 0.020 * 0.9810 + 10C1 * 0.021 * 0.989

              = 0.8171 + 0.1667

              = 0.9838

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