Answer to Question #296636 in Statistics and Probability for Tesema

Question

On the average, six people per hour use a self services banking fasility during the prime shopping hours in a department store. Assuming the arrival of customers is random and independent; What is the probability that; One person will use the facility during 30 seconds interval?

Answer 1

The rate is 6 people per hour. In 30 seconds, the parameter $\lambda=30\times{6\over 3600}=0.05\approx 1 \space person$

Let $X$ be a random variable representing the number of users of the banking facility then, $X\sim Poisson(\lambda=1)$.

We find,

$p(x=1)={e^{-1}1^1\over1!}=e^{-1}=0.3679$    

Therefore, the probability that one person will use the facility during 30 seconds interval is 0.3679