Find the indicated probabilities using the geometric distrib

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.)

Solution

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]