Question

Reference: Statistical Quality Control 7th Edition by Douglas C. Montgomery

A production process that appears to have a constant .06% nonconforming output. Every two hours, a random sample of 100 items is taken and measured. If two or more nonconforming items are found, all facility employees are required to watch a 20 minute video on the importance of doing work to specification. Following that reeducation effort, this process is reset and restarted. What is the probability that two or more nonconforming items will be found in a random sample?

Answer 1

Binomial Distribution

n = 100

p = 0.06

q = 1 -p = 0.94

P(X2) = 1 - [P(X=0) + P(X=1)]             (1)

P(X=0) = qⁿ = 0.94¹⁰⁰ = 0.002055          (2)

   (3)

Substituting (2) & (3), equation 91) becomes:

P(X2) = 1 - 0.0152

            = 0.9848

So,

Answer is:

0.9848