Question

Suppose that on average, there are 1.2 defects per 75 square foot roll of wallpaper and the number of defects follows a Poisson distribution. Determine the probability that a 25 square foot roll of wallpaper will have one or fewer defects?

Answer 1

There are 1.2 defects per 75 square foot roll.

so for 25 square foot roll, there will be 0.4 defects.

$\lambda = 0.4$

$P(X\leq 1) = P(X=0)+P(X=1) = e^{-0.4}\frac{0.4^0}{0!}+ e^{-0.4}\frac{0.4^1}{1!} = 0.9384$