Find the indicated probabilities using the geometric distribution or Poisson dis
ID: 3389785 • Letter: F
Question
Find the indicated probabilities using the geometric distribution or Poisson distribution Then determine if the events are unusual convenient use a Poisson probability table or technology to find the probabilities. A newspaper finds that the mean number of typographical errors per page is five. Find the probability that exactly four typographical errors are found on a page, at most four typographical errors are found on a page, and more than four typographical errors are found on a page P(exact four typographical errors are found on a page) = (Round to four decimal places as needed.)Explanation / Answer
THIS IS A POISSON DISTRIBUTION, as the mean is given and is constant per page.
a)
Note that the probability of x successes out of n trials is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 5
x = the number of successes = 4
Thus, the probability is
P ( 4 ) = 0.17546737 [ANSWER]
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b)
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 5
x = the maximum number of successes = 4
Then the cumulative probability is
P(at most 4 ) = 0.440493285 [ANSWER]
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c)
Note that P(more than x) = 1 - P(at most x).
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 5
x = our critical value of successes = 4
Then the cumulative probability of P(at most x) from a table/technology is
P(at most 4 ) = 0.440493285
Thus, the probability of at least 5 successes is
P(more than 4 ) = 0.559506715 [ANSWER]
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