A quality inspector at a glass manufacturing company inspect

A quality inspector at a glass manufacturing company inspects sheets of glass to check for any slight imperfections. Suppose that the number of flaws in a glass sheet has a Poisson distribution with parameter = 0.5 . If a sheet has more than one flaw, it must be scrapped.

(a) What percentage of sheets must be scrapped?

(b) Given that a sheet has at least one flaw, what is the probability that the sheet will be scrapped?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
a)
P( X < = 1) = P(X=1) + P(X=0)
= e^-0.5 * 0.5 ^ 1 / 1! + e^-0.5 * 3 ^ 0 / 0!
= 0.9098
P( X > 1) = 1 -P ( X <= 1) = 1 - 0.9098 = 0.0902