10. HW 5 A textile manufacturing process finds that on average, 2 flaws occur pe
ID: 3307352 • Letter: 1
Question
10. HW 5
A textile manufacturing process finds that on average, 2 flaws occur per every 50 yards of material produced.
What is the probability of exactly 2 flaws in a 50-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 50-yard piece of material? (Round your intermediate calculations and final answer to 4 decimal places.)
What is the probability of no flaws in a 25-yard piece of material? (Round your intermediate calculations and final answer to 4 decimal places.)
A textile manufacturing process finds that on average, 2 flaws occur per every 50 yards of material produced.
Explanation / Answer
Solution:-
Model the number of flaws with a poisson random variable. P(N = n) = e^(-m) m^n / n!
Where m is the expected number of flaws, which is 2 per 50 yards.
a. P(N = 2) = e^(-2) (2)^(2) / 2! = 0.2707
b. P(N < 2) = P(N = 0) + P(N = 1) + P(N = 2) = 0.6707
c. P(N = 0 | m=2) = 0.3679
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