Question 1150893: Textbook authors and publishers work very hard to minimize the number of errors in a text. However, some errors are unavoidable. Mr. J. A. Carmen, statistics editor, reports that the mean number of errors per chapter is 0.8 . What is the probability that there are less than 2 errors in a particular chapter?
Answer by MathLover1(20850)   (Show Source):
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Let the event an  appearing in a chapter be a  .
Let " " represent the number of .
The number of errors in a chapter can be either  , , ,...
==> "" can carry the values ,,, ,...
==> "" is a discrete random variable with range = { ,, },..... [Countably infinite]
The probability distribution of "" is a   .
Since there are a large number of trials all of which are identical and independent with only two possible outcomes in each trial, either a success (there being an error) or a failure (there not being an error), with the probability of success in all the trials remaining the same all thought.
The probability function of a Poisson distribution
==> 
Parameter of the distribution
==> Mean of the distribution
==> Mean number of errors per chapter =
==> m = 
Therefore 
Probability that there are less than 2 errors in a chapter
==>
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= 
= 
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= approximately
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