One(1) in twenty(20) microchips is defective. Fora Quality Control analysis, 50

Question

One(1) in twenty(20) microchips is defective. Fora Quality Control analysis, 50 chips are analized. 1.What is the probabilitythat none(0) are defective. 2.How many microchips will be defective. 3.What is the probability that one(1) is defective. The microchips are analized consecutively. 4.How many microchips must be analized until reaching thefirst defective. 5.What is the probability that the first defective microchipis the fourth analized. 6.What is the standard deviation of the instant in which thefirst defective microchip appears. One(1) in twenty(20) microchips is defective. Fora Quality Control analysis, 50 chips are analized. 1.What is the probabilitythat none(0) are defective. 2.How many microchips will be defective. 3.What is the probability that one(1) is defective. The microchips are analized consecutively. 4.How many microchips must be analized until reaching thefirst defective. 5.What is the probability that the first defective microchipis the fourth analized. 6.What is the standard deviation of the instant in which thefirst defective microchip appears.

Explanation / Answer

Question 1: probabilitythat none(0) are defective. Let X = # of defective chips. X ~ Binomial (n = 50, p = 1/20 =0.05) Let q = 1- p = 0.95 P(X = 0) = q20 = 0.9520= 0.3585

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