On the average two new checking accounts are opened per day

On the average two new checking accounts are opened per day at the Farmer’s Bank. What is the likelihood that for a particular day: (Hint: Since the average/mean is given, solve using the Poisson).

a.   no new accounts are opened?

b.   at least one new account is opened?

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 =    2      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.135335283 [answer]

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b)

P(at least one) =1 - P(0) = 0.864664717 [answer]