A production process produces 2% defective parts. a sample of 5 parts from the production is selected. what is the probability that the sample contains exactly two defective parts? use the binomial probability function and show your computations to answer this question.

Question

Mathematics

Evie

15 October, 06:02

A production process produces 2% defective parts. a sample of 5 parts from the production is selected. what is the probability that the sample contains exactly two defective parts? use the binomial probability function and show your computations to answer this question.

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Hancock · Answer 1

Possible outcomes: defective/non defective

Applying Binomial distribution equation

p (x) = [N!/x! (N-x) !] * (p^x) (q) ^N-x

Where,

p = 2% = 0.02

N = 5

And then,

q = 1-p = 1-0.02 = 0.98

x = 2

N-x = 5-2 = 3

Substituting;

p (2) = [5!/2! (5-2) !]*0.02^2*0.98^3 = 0.00376 = 0.376%