[Math] How to apply the example of cars passing through a road to the Poisson distribution

Question

Cars pass through a road junction according to a Poisson distribution.
An average of 5 cars per minute pass through the junction.

a) What is the probability that exactly one car passes through the
junction in a certain minute?

b) What is the expected number of cars to pass through in three
minutes?

c) What is the probability that exactly the expected number from (b)
pass through in a certain three minute period?

I used the formula $f(x,\lambda) = \frac{\lambda^x e^{-\lambda}}{x!}$

For part a $f(1,5) = \frac{5 e^{-5}}{1!} = 0.0337$…..

For part b) $\lambda = 5$ for one minute, so $\lambda = 5 \cdot 3 = 15$ for 3 minute

For part c) $f(15,15) = \frac{15^{15} e^{-15}]}{15!} = 0.10244$…

Is my method and the answers correct?

Answer 1

I think your answers are all right.