poisson distribution

Mar 2010
4
0
line is tested with average of three flaws per kilometer.
a) find probability that exactly 2 flaws found.
i got 0.61 as an answers but others got .224 not sure what i did wrong.
b) how do i calculate the formula if i am testing 3 kilometers not just one?
i assume i put 9 as lambda and three for x however when i do the calculation for f(0) i get 1.234x10 to the negative 4?:(
 

matheagle

MHF Hall of Honor
Feb 2009
2,763
1,146
.224041808.....

Poisson with lambda=3 is

\(\displaystyle P(X=x)={e^{-3}3^x\over x!}\)

So \(\displaystyle P(X=2)={9e^{-3}\over 2}\)