Arrivals in a unversity advising office during the week of r

Arrivals in a unversity advising office during the week of registration are known to follow a Poisson distribution with an average of 4 people arriving each hour:

a. What is the probability that exactly 4 people will arrive in the next hour?

b. What is the probability that exactly 5 people will arrive in the next hour?

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

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 =    5      
          
Thus, the probability is          
          
P (    5   ) =    0.156293452 [answer]