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 ? be a random variable representing the number of defective television set in the random sample of 10.

a. Explain why X may be treated as a binomial random variable:  Identify n (the number of trials):  Specify (in words) which event would be defined as a “success”:  Explain why the trials may be considered independent:  Give the value of p (the probability of a success):

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 _______

Answer 1

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 defactive television set per sample would be approximately 0.2