Question

1.   The number of calls coming into a hotel’s reservation center averages three per minute.

a. Find the probability that no calls will arrive in a given one-minute period.

b. Find the probability that at least two calls will arrive in a given one-minute period.

Answer 1

Let $X=$ the number of calls arriving in a given one minute period: $X\sim Po(\lambda t)$

Given $\lambda=3, t=1$

$\lambda t=3(1)=3$

a.

$$P(X=0)=\dfrac{e^{-3}\cdot3^0}{0!}=e^{-3}\approx0.049787$$

b.

$$P(X\geq 2)=1-P(X=0)-P(X=1)$$ $$=1-\dfrac{e^{-3}\cdot3^0}{0!}-\dfrac{e^{-3}\cdot3^1}{1!}=1-4e^{-3}\approx0.800852$$