There are two question related to the above information is;
1) What is the mean or expected number of customers that will arrive in a five-minute period?
Answer:
to calculate the mean, customers per minute is equal to 0.4
mean for that will arrive in a five minute period = 0.4 x 5 = 2
thus, the answer is 2.
2) Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (1) and compute the probabilities that exactly 0, 1, 2,and 3 customers will arrive during a five-minute period.
Given X Poisson (Mean =2 in 5 minutes)
P(X=x) =(2^x)x exp(-2)/x!
P(X=0)=(2^0) x Exp(-2)/1! = 0.1353353
P(X=1)=(2^1) x Exp(-2)/1! =0.2706706
P(X=2)=(2^2) x Exp(-2)/2! = 0.2706706
P(X=3)=(2^3) x Exp(-2)/3! = 0.180447
