In each of the following situations, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case. (a)An auto manufacturer chooses one car from each hour’s production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples, ripples, etc.) in the car’s paint.   (b)The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty; X is the number who says “Yes.”   (c)Joe buys a ticket in his state’s Pick 3 lottery game every week; X is the number of times in a year that he wins a prize.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.