Question

Shipments of television set 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.

1. Explain why X is a binomial random variable:

• Specify, in words, what is a trial in this scenario
• Identify n (the number of trials)
• Specify, in words, which outcome of trial would be defined as a “success”
• Explain why p (is the probability of success) is the same for every trial
• Identify p (the probability of success):

2. What is the probability that this shipment results will consider to be satisfactory? (Use a table or the formula).

3. What is the expected value of the number of defective television set in this sample?

4. Fill in the blanks in the following sentence:                                                                                According to the Law of Large Numbers, if we 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

Binomial will be used in this question

In general, if the random variable X follows the binomial distribution with parameters n ∈ ℕ and p ∈ [0,1], we write X ~ B(n, p). The probability of getting exactly k successes in n independent Bernoulli trials is given by the probability mass function:

for k = 0, 1, 2, ..., n, where

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