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