On average, 80 customers arrive at a fast food establishment’s drive-through win

Question

On average, 80 customers arrive at a fast food establishment’s drive-through window each hour of operation. The probability of a customer arriving at the window is the same for any two periods of equal length and the arrival of a customer during one time period is independent of the arrival of a customer during any other non-overlapping time period.

(a) What is the probability of 10 customers arriving in a fifteen-minute period of operation?

(b) What is the probability of at least 1 customer arriving in a fifteen-minute period of operation?   

Explanation / Answer

This is Poison distribution P(x)=e^-lembda*lembda^x/x!

a. Here x=10 and lembda=15 p(x=10)=0.0486

b. Here x=1 and lembda =15 P(x>=1)=1.000

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