Question

Shipments of TV sets that arrive at a factory have a varying levels of quality. In order to decide whether to accept a particular shipment, inspectors randomly select a sample of 15 TVs and test them; if no more than one TV in the sample is defective, the shipment is accepted. Let X be a random variable representing the number of defective staples in the random sample 15.

a. Explain why X may be treated as a binomial random variable:

•Identify n (the number of trails):

•Specify in words which event would be defined as a “success”

•Explain why the trails may be considered independent:

•Give the value of p (probability of a success)

b. What is the probability that shipment is accepted? ( Use a table or the formula)

c. What is the expected value of the number of defective TV set in the sample?

d. Fill this 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 TV sets per sample would be approximately ___.

Answer 1

a) X may be treated as binomial random variable because the parameter for a variable to be binomial is the number of trials n and the probability of success p

For X the number of trials is n = 15

let p be the probability of success ( TV set to be defective )

Trials can be considered independent because of the probability that tv set is defective is independent of the other TV sets.

Let P be the probability of success

b)The probability that shipment is accepted =

The probability that shipment is accepted =

c) Expected number of defects = np= 15p

d) According to the Law of Large Numbers, if we have obtained many different simple random samples of size 15 from this shipment, the average number of defective TV sets per sample would be approximately normal and equal to 15p