Find the indicated probabilities using the geometric distrib

Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. Ifconvenient, use the appropriate probability table or technology to find the probabilities.

A newspaper finds that the mean number of typographical errors per page is nine.Find the probability that (a) exactly five typographical errors are found on a page, (b) at most five typographical errors are found on a page, and (c) more than five typographical errors are found on a page.

Solution

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 =    9      
          
x = the number of successes =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.060726879 [ANSWER]

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B)

Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    9      
          
x = the maximum number of successes =    5      
          
Then the cumulative probability is          
          
P(at most   5   ) =    0.115690521 [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 =    9      
          
x = our critical value of successes =    5      
          
Then the cumulative probability of P(at most x) from a table/technology is          
          
P(at most   5   ) =    0.115690521
          
Thus, the probability of at least   6   successes is  
          
P(more than   5   ) =    0.884309479 [ANSWER]