Question

A production manager knows that 95% of components produced by a particular manufacturing process have no defect. Six of these components selected randomly and examined,

- What is the probability that two of these components havedefect?
- What is the probability that at least four of these components have a defect?
- What is the expected number of defective sets?
- Interpret the result of all three parts of this question.

Answer #1

Let X = defective components.

p = probability of defective components = 5% = 0.05

n = no. of component selected = 6

X follows Binomial distribution with parameter n and p. The pmf of X is,

a.

b.

c.

Expected number of defective sets = np = 6* 0.05 = 0.3

d.

a. Probability that 2 components out of 6 are defective is 0.0305

b. Probability that more than 4 components are defective is 0.0000864, which is very small.

c. On an average there are 0.3 defective components out of 6 selected components.

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