POISSON Distribution, probability there is no flaw

Question

I am having difficulty with part b and c. I have got part a.

This is the question:

For part a) I have $P(x=2) = (e^{-0.1} * (0.1)^2)/2!$

What do I do for part b?

Answer 1

Convert the rate to $\lambda = 1$ flaw per $10m^2$ and then use the formula $\mathbb{Pr}[X = 0] = \frac{\lambda^0 e^{-\lambda}}{0!} = e^{-\lambda}$

Answer 2

Hint:

• If there is a mean $0.1$ flaws per square metre, there is a mean $1$ flaw per $10$ square metres

• If there is a mean $0.1$ flaws per square metre, there is a mean $10$ flaws per $100$ square metres

Use the Poisson distribution again.