A textile manufacturing process finds that on average, two flaws occur per every

Question

A textile manufacturing process finds that on average, two flaws occur per every 50 yards of material produced. a. What is the probability of exactly two flaws in a 50-yard piece of material? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability b. What is the probability of no more than two flaws in a 50-yard piece of material? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability c. What is the probability of no flaws in a 25-yard piece of material? (Do not round intermediate calculations. Round your final answer to 4 decimal places.) Probability

Explanation / Answer

POSSION DISTRIBUTION
pmf of P.D is = f ( k ) = e- x / x!
where
= parameter of the distribution.   
x = is the number of independent trials
I.
mean =
= 2
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.
for 25 yard piece of material the mean rate is 1
P( X = 0 ) = e ^-1 * 1^0 / 0! = 0.3679

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