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A lot contains several thousand components, l 1% of which are defective. Ten components are sampled from the lot. Let X represent the number of defective components in the sample. X can best be modeled by what distribution ? (include the appropriate parameter values)

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Answer #1

X can best be modelled by Binomial Distribution because we can assume that a particular component being defective is independent of all other 9 components being defective. This is valid assumption because the given lot contains several thousands of components and hence there is expected to be no correlation between any two subsets of components being defective. Also, probability of a component being defective is uniform across all the components i.e. for each component, p = 0.11. Therefore, X can best be modelled with Binomial Distribution having N = 10 and Probability of Success(p) = 0.11, where "success" is defined as " A component is defective".

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