Question

On average, 1.7 students uses the ATM machine any 30 minute interval. Find the probability of exactly 3 students using the ATM machine during any 30 minute interval.

Answer 1

Let $X=$ the number of students using the ATM machine : $X\sim Po(\lambda)$

$$P(X=x)=\dfrac{e^{-\lambda}\cdot \lambda^x}{x!}$$

Given $\lambda=1.7$

$$P(X=3)=\dfrac{e^{-1.7}\cdot 1.7^3}{3!}=0.14959$$