4 A machine shop has 400 drill presses and other machines in

4. A machine shop has 400 drill presses and other machines in constant use. The probability that a machine will become inoperative during a given day is 0.01.   

a.) What is the probability that at least two machines will be inoperative during a particular day?

b.) What is the probability that at exactly 3 machines will be inoperative during a particular day?

Solution

a)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative poisson distribution table or technology, matching          
          
u = the mean number of successes =    4      
          
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.091578194
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.908421806 [ANSWER]

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b)

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 =    4      
          
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.195366815 [ANSWER]