Question

On the average 10 customers arrive each half-an-hour at the checkout counter at a local retail store.

Part A: Prepare the probability distribution table in Excel. What is the probability that no more than 7 customers arrive at the checkout counter in 30 min.?

Part B: Prepare the probability distribution table in Excel. What is the probability that no less than 3 customers arrive at the checkout counter in 18 min.?

Part C: Prepare the probability distribution table in Excel. What is the probability that at least 4 but less than 10 customers arrive at the checkout counter in 22.5 min.?

Please use Excel and show formulas used.

Answer 1

a) for 30 minutes expected customers =10

hence  probability that no more than 7 customers arrive at the checkout counter in 30 min =P(X<=7)

=poisson(7,10,true) =0.2202

b)

probability that no less than 3 customers arrive at the checkout counter in 18 min =P(X>=3)

=1-P(X<=2)=1-poisson(2,10*18/30,true)=0.9380

c)

probability that at least 4 but less than 10 customers arrive at the checkout counter in 22.5 min

=P(4<=X<10)=poisson(9,10*22.5/30,true)-poisson(3,10*22.5/30,true) =0.7173