Suppose that, on average, 2 people in 1000 makes a numerical error in preparing his or her income tax return. If 6000 returns are selected at random and examined, find the probability that 7, 8, or 9 of them contain an error. Click here to view page 1 of the table of Poisson probability sums. Click here to view page 2 of the table of Poisson probability sums. The probability that 7, 8, or 9 income tax returns contain an error is. (Round to four decimal places as needed.)
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.
Let random variable X represent the number of forms containing numerical error out of 6000 forms selected at random.
If a form contain an error, it is considered as success.
Probability of a success in each trial is .
Because trails are independent, X has a binomial distribution with parameters .
But, here is too small which is close to 0. number of trials, n=6000 is large and is finite.
Therefore, using Poisson approximation, X has a Poisson distribution with parameter
The probability mass function of X is,
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