A textile manufacturing process finds that on average 2 flaw

A textile manufacturing process finds that on average, 2 flaws occur per every 170 yards of material produced.

What is the probability of exactly 2 flaws in a 170-yard piece of material? (Round your intermediate calculations and final answer to 4 decimal places.)

What is the probability of no more than 2 flaws in a 170-yard piece of material? (Round your intermediate calculations and final answer to 4 decimal places.)

What is the probability of no flaws in a 68-yard piece of material? (Round your intermediate calculations and final answer to 4 decimal places.)

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 = 2 ) = e ^-2 * 2^2 / 2! = 0.2707
b)
P( X < = 2) = P(X=2) + P(X=1) + P(X=0) +
= e^-2 * 2 ^ 2 / 2! + e^-2 * 2 ^ 1 / 1! + e^-2 * ^ 0 / 0! +   
= 0.6767
c)
P( X = 0 ) = e ^-1 * 1^0 / 0! = 0.3679