2 Aproduction process s known to produce 5% defective nens. A sample of 20 items

Question

2 Aproduction process s known to produce 5% defective nens. A sample of 20 items is selected from the process. What is the probability distribution of the number of defective tems in the sample? (Circle one) (1 point) a) Geometric b) Binomial c) Poisson d) Negative Binomial ) None of the above 3. Suppose a certain supplier of vehicle windshields has discovered that each averages 4 surface flaws The number of surface flaws per windshield can be approximated by a Poisson probability distribution. (2 points each a) What is the probability that there are no surface flaws in a windshield? b) What is the probability that there are less than 3 surface flaws in a windshield? c) What is the probability that there are more than 2 surface flaws in a windshield?

Explanation / Answer

#2.
This is Binomial probability distribution because any selected item will either be defective or non defective.

#3.
Poisson's Distribution Formula:
P(X = x) = (e^-) (^x) / x!
= 4

a)
P(X = 0) = e^-4*(4^0)/0! = 0.0183

b)
P(X = 0) = e^-4*(4^0)/0! = 0.0183
P(X = 1) = e^-4*(4^1)/1! = 0.0734
P(X = 0) = e^-4*(4^2)/2! = 0.1465

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.2381

c)
P(X > 2) = 1 - P(X <=2)
P(X <= 2) = P(X < 3)
P(X > 2) = 1 - 0.2381 = 0.7619

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