For a certain type of fabric,the average number of defects in each square foot of fabric is 0.9.Find the probability that a randomly selected square foot of the fabric will contain more than one defect.
A)0.5934
B)0.2275
C)0.6341
D)0.7725
E)0.1647

Question

Quizplus · Accepted Answer

The number of defects in a square foot of fabric follows a Poisson distribution with parameter λ = 0.9. We want to find P(X > 1), where X is the number of defects in a square foot.

Using the Poisson probability formula: 
P(X > 1) = 1 - P(X ≤ 1) 
= 1 - [P(X = 0) + P(X = 1)] 
= 1 - [e^(-λ)λ^0/0! + e^(-λ)λ^1/1!] 
= 1 - [e^(-0.9)0.9^0/0! + e^(-0.9)0.9^1/1!] 
= 1 - [0.4066 + 0.3659] 
= 0.2275

Therefore, the correct choice is B.

For a Certain Type of Fabric,the Average Number of Defects