Question 1043335: Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.
A newspaper finds that the mean number of typographical errors per page is four. Find the probability that (a) exactly six typographical errors are found on a page, (b) at most six typographical errors are found on a page, and (c) more than six typographical errors are found on a page.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! For typographical errors, it is a Poisson distribution with small number of errors that can theoretically be infinite, are considered to be independent, integer amounts, and occurrence is proportional to interval length.
for lambda=4, the probability of x events' occurring is e^(-lambda)*lambda^x/x!
probability of 6 is e^(-4)4^6/6!
This is 0.0183*4096/720=0.104
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probability of 5 is e^(-4)4^5/5!=0.1563
probability of 4 is (e^(-4)4^4/4!=0.1954
probability of 3 is e^-4)4^3/3!=0.1954
probability of 2 is e^(-4)4^2/2=0.1465
probability of 1 is e^(-4)*4=0.0733
probability of 0 is e^(-4)=0.0183
At most 5 is the sum, or 0..785
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At most 6 is 0.785+ probability of 6, or 0.104 from above, and that is 0.889
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More than 6 is the complement of 1-0.889 or 0.111.
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