A collection of 120 critical components is available for your use. It is generally known that the rate of occurrence of defects is 5% and that on the average 1 out of 20 will be defective. If you are to select 40 out of the 120 for use find the following probabilities using a) Binomial b) Hypergeometric and c) Poisson

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Mathematics

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1 June, 23:14

A collection of 120 critical components is available for your use. It is generally known that the rate of occurrence of defects is 5% and that on the average 1 out of 20 will be defective. If you are to select 40 out of the 120 for use find the following probabilities using a) Binomial b) Hypergeometric and c) Poisson

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Answers (1)

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Twig · Answer 1

Answer:a

a) 0.2777

b) 0.3377

c) 0.2707

Step-by-step explanation:

binomial-

n=40

p=0.05

P (X = 2) = C (40,2) * 0.05^2 * (1-0.05) ^38 = 0.2777 (answer)

hypergeometric-

total component, N=120 out of which 6 are defective and 114 are non defective

P (X=2) = C (6,2) * C (114,38) / C (120,40) = 0.3377

Poisson-

Mean/Expected number of events of interest: λ = np=40*0.05 = 2

P (X = 2) = e^ - (2*2^2/2!) = 0.2707