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 _______

Explanation / Answer

a. Here it is given that if no more than one television set in the sample is defective, the shipment is accepted.

This is binomial distribution with n=10 and p=0.02

so  P(X<=1) = P(X=0) + P(X=1) = 0.8171 +0.1667 = 0.9838

b. Expected value is np=10*0.02=0.2

c. According to the Law of Large Numbers, if we have obtained many different simple random samples of size 10 from this shipment, the average number of defective television set per sample would be approximately 0.2.

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