Acollection 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

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

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step-by-step explanation: