62% of VCRs of a Certain Type Are Defective

question 114

Essay

6.2% of VCRs of a certain type are defective. Let the random variable X represent the number of defective VCRs among 200 randomly selected VCRs of this type. Suppose you wish to find the probability that X is equal to 8. Does the random variable X have a binomial or a Poisson distribution? How can you tell? If X has a binomial distribution, would it be reasonable to use the Poisson approximation? If not, why not?

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Definitions:

Compound

A substance formed from two or more elements chemically united in fixed proportions; or, in a linguistic context, a term made up of two or more words functioning as a single unit.

Atomic

Constituting an undivided whole; elementary, with reference to particles or concepts.

Truth-functional Compound

A complex proposition in logic that is made up of simpler propositions and whose truth-value depends solely on the truth-values of these simpler propositions.

Quantifier

In logic, symbols that specify how many objects in the universe of discourse satisfy a given condition.