So I got a summer homework package from school

, and I need to teach myself Poisson Distribution before school starts. So here's the question I've been stuck on for a while. (I need help on b.)

The number of faults in glass sheets occur at a rate of 2.1 per sq. metre. If a 1x1 sq. m glass sheet contains at least 3 faults it is returned to the manufacturer.

a) Find the probability that a 1x1 sq. m sheet is returned to the manufacturer.

My answer:

$\displaystyle P(X > 2) = 1 - P(0) - P(1) - P(2)$

$\displaystyle P(X > 2) = 1 - e^{-2.1}(1+2.1+\frac{2.1^{2}}{2})$

$\displaystyle P(X > 2) = 0.3504$

b) Six such glass sheets are inspected. What is the probability that at least half of them are returned to the manufacturer? (Here's the answer provided: 0.6817)

It would be nice if you can show me the work and proper notation, because I barely have a clue.

Thanks.