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 fewer than 5 people will use the facility during a randomly selected hour?

Answer 1

Let $X=$ the number of customers using a self services banking fasility: $X\sim Po(\lambda t).$

Given $\lambda t=6.$

$$P(X<5)=P(X=0)+P(X=1)+P(X=2)$$

$$+P(X=3)+P(X=4)=\dfrac{e^{-6}(6)^0 }{0!}+\dfrac{e^{-6}(6)^1 }{1!}$$

$$+\dfrac{e^{-6}(6)^2 }{2!}+\dfrac{e^{-6}(6)^3 }{3!}++\dfrac{e^{-6}(6)^4 }{4!}$$

$$=e^{-6}(1+6+18+36+54)=115e^{-6}$$

$$\approx 0.2850565$$