I am the only bank teller on duty at my local bank. I need to

run out for 20 minutes, but I do not want to miss any customers.

Suppose the arrival of customers can be modeled by a Poisson

distribution with mean 3 customers per hour. What’s the probability

that exactly 3 customers will arrive in the next 20 minutes? Give

your answer to 4 decimal places.

Let X be the arrival of customer. X follows Poisson distribution with mean 3 customers per hour. i = 3 customers per hour 3 per minute 60 3 -x 20 per 20 minute 60 =1 per 20 minute = The probability mass function of Poisson distribution is. P(X = x)= *2* x! The probability that exactly 3 customers will arrive in the next 20 minutes is, e-’13 P(X = 3) = 3! 0.3679×1 6 0.0613