Question

The number of customers that enter a bank follows a Poisson distribution with an average of 30 customers per hour. What is the probability that exactly 3 customers would arrive during a 12 minute period?

Select one:

a. 0.4211

b. 0.1008

c. 0.2586

d. 0.1404

e. 0.0892

Answer 1

Solution :

Let X represents the number of customers arriving at a bank.

Given that, X follows poisson distribution with average rate of 30 customers per hour.

We have to obtain P(X = 3) in t = 12 minutes.

According to poisson process, the probability of occurrence of exactly x events in time t is given by,

Where, λ is the rate of occurrence of the event.

We have, λ = 30 customers/hour

t = 12 minutes = 12/60 = 0.2 hour

λt = 30 × 0.2 = 6

Hence, the probability that exactly 3 customers would arrive during a 12 minute period is 0.0892.

Hence, option (e) is correct.

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