SOLUTION: The customer service department of HSBCC Bank receives the complaints following a Poisson distribution with the mean rate of two complaints per day. (i) What is the probability of

Question 1150679: The customer service department of HSBCC Bank receives the complaints following a Poisson distribution with the mean rate of two complaints per day.
(i) What is the probability of at most two complaints per day?
(ii) Assume that a week has five working days. What is the probability that a randomly selected week has three days with at most two complaints per day?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
at most 2 complaints is 0, 1, 2
for 0 prob is e^(-2)*2^0/0!
this is e^(-2) or 0.1353
for 1 p(1) is e^(-2)*2^1/1! or twice the above or 0.2707
for 2, it would be e^(-2)*2^2/2!
or the same as for p(1) or 0.2707
sum is 0.6767
For 3 days with at most 2 complaints per day is a binomial distribution
5C3*0.6767^3*0.3233^2=0.3239, the 5C3 or 10 are the number of ways it can occur in 5 days.
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