Kevins Karpet Kompany offers their premium carpet at a barga

Kevin\'s Karpet Kompany offers their premium carpet at a bargain price. It has been discovered, however, that Kevin\'s premium carpets have a flaw ( loose shag) in every 150 square feet, on average, Assuming that the number of flaws you will find in the premium carpet you buy from Kevin has a Poisson distribution, what is the probability that the 225 square feet of premium carpet you\'re just bought from Kevin will have at most one flaw.

[answer is .5578]

Can you show step by step how to solve this problem?

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
Kevin\'s premium carpets have a flaw ( loose shag) in every 150 square feet
Mean rate for 225 square feet of premium carpet 250/150 = 1.667
P( X < = 1) = P(X=1) + P(X=0)
= e^-1.667 * 1.667 ^ 1 / 1! + e^-1.667 * 5 ^ 0 / 0!
= 0.5036