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,

1. What is the probability that two of these components havedefect?
2. What is the probability that at least four of these components have a defect?
3. What is the expected number of defective sets?             
4. 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.