A new automated production process averages 1.8 breakdowns per day. Because of the cost associated with a breakdown, management is concerned about the possibility of having three or more breakdowns during a day. Assume that breakdowns occur randomly, that the probability of a breakdown is the same for any two time intervals of equal length, and that breakdowns in one period are independent of breakdowns in other periods. What is the probability of having three or more breakdowns during a day? Step 1 It is given that the probability of a breakdown is the same for time intervals of equal length and that breakdowns are independent of one another. These are the necessary properties for a Poisson experiment. Recall the formula for calculating the probability f(x) of x occurrences in a time interval when there is an average of μ occurrences in time intervals of the same length. f(x) =  μxe−μ x! There is an average of 1.8 breakdowns per day and of concern is having three or more breakdowns per day. Therefore,  μ =  .

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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.