A textile mill produces fabric used in the production of dre

A textile mill produces fabric used in the production of dresses. Each dress is assembled from patterns that require 2 square yards of material. Quality monitoring typically finds 12 defects (snagged threads, color splotching) per 100 square yards when testing sections of this fabric. Determine whether the following statement is true or false. If the statement is false, explain why it is false.

A Poisson model implies that the probability of a defect in the material used to make a dress is

2times×12/100.

Choose the correct answer below.

A.

False, because

lambdaequals=2times×12/100

and the probability of at least one defect is 0.787

B.

False, because

lambdaequals=0.12

and the probability of at least one defect is 0.113

C.

True

D.

False, because

lambdaequals=0.24

and the probability of at least one defect is 0.213

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

P( X < 1) = P(X=0) +   
= e^-0.24 * 1 ^ 0 / 0!
= 0.7866

P( X > = 1 ) = 1 - P (X < 1) = 0.2134

D.

False, because

lambdaequals=0.24

and the probability of at least one defect is 0.213