Problem

Delivery trucks arrive independently at the Floorstore Regional distribution center with various consumer items from the company’s suppliers. The mean number of trucks arriving per hour is 20. Given that a truck has just arrived answer the following:

a) What is the probability that the next truck will not arrive for at least 5 minutes?

b) What is the probability that the next truck will arrive within the next 2 minutes?

c) What is the probability that the next truck will arrive between 4 and 10 minutes?

Attempt

$\displaystyle \mu = \lambda^{-1} \Rightarrow \lambda = 3$ min to wait

$\displaystyle P(T > 5)=e^{-3 \cdot 5}$