Question

The number of customers arriving per five minute period at a certain shop has a Poission distribution with a mean lambda equal to 2. What is the probability that there will be no customers arriving in the next five minute period? (Give your answercorrected to four decimal points as 0.xxxx)

Answer 1

Given that, no. of customers arriving per five minutes follows Poisson distribution with mean = 2

Therefore, arrival rate of customer is 2 per five minutes.

Let X be the random variable representing the no. of arrivals customers in t = 5 minutes.

The probability mass function of Poison distribution is given by,

Where X = 0,1,2,3.....................

What is the probability that there will be no customers arriving in the next five minute period ? i.e. find, P(X=0)

Therefore, 0.1353 is the probability that there will be no customers arriving in the next five minute period.