Exponential distribution problem

**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

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