For a certain type of fabric, the average number of defects in each square foot of fabric is 0.3. Find the probability that a randomly selected square foot of the fabric will contain more than one defect.
A)0.0369
B)0.7778
C)0.0333
D)0.9631

Question

Quizplus · Accepted Answer

The probability of more than one defect can be found using the Poisson distribution formula. Given the average rate (λ) of 0.3 defects per square foot, the probability of getting more than one defect (k > 1) is 1 minus the probability of getting 0 or 1 defects. Using the Poisson formula, P(k; λ) = (e^(-λ) * λ^k) / k!, for k = 0 and k = 1, we calculate these probabilities and subtract from 1. The calculation for 0 and 1 defects gives us a combined probability, which when subtracted from 1, gives the probability of having more than one defect. The correct calculation aligns with choice A, 0.0369, as the probability of having more than one defect in a square foot of this fabric.

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