A computer factory receives large shipments of chips. Different shipments have q

Question

A computer factory receives large shipments of chips. Different shipments have quality. In order to decide whether to accept a particular shipment, inspectors randomly select a sample of 20 computer chips and test them;if at least two chips in the sample are defective, the shipment is returned. Suppose a very large shipment arrives in which 5% of the computer chips are defective. Let X be a random variable representing the number of defective chips in a random sample of 20. 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: Calculate p, the probability of a success: b. What is the probability that this shipment is accepted? (Use a table or the formula). C. What is the expected value of the number of defective chips in this sample? D. Fill in the blanks: "For a large shipment contains 5,000 computer chips, the average number of defective items in this sample would be approximately equal to ____ computer chips"

Explanation / Answer

a.

n ( numberof trials ) = 20

Here we are interested in whether the shipment s accepted or not. Here the acceptance of shipement is considered as a success.

Here inspector randomly select a 20 computer chips and test them. Here selection of chips is not dependent on each other, it is random. Hence here trials are considered tto be independent.

p = probability of success = probability of defective chips = 0.05

b. Here shipment will be accepted if less than 2 chips are deective.

p ( X = x ) = nCx px ( 1 - p )n-x

p ( x < 2 ) = p ( x = 0 ) + p ( x = 1 )

= 20C0 0.050 ( 1 - 0.05 )20-0   + 20C1 0.051 ( 1 - 0.05 )20-1

= 0.3585 + 0.3774

= 0.7359

Probability of acceptance of shipment = 0.7359

c. Expected value of number of defective chips = n * p = 20 * 0.05 = 1

d. Here n = 5000

Average number of defective items = n * p = 5000 * 0.05 =250

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