If we have a lot which is made up of 100 products (50 products from each production line), what is P(x<=1), where x is number of nonconforming product in a sample size of 10 products? (No approximation methods, Calculation with three digits after decimal point)?.

Can the production line manager say the lines meet the Six Sigma Requirements? Why?

Consider Production Line 1, Nonconformities occur in productions according to a Poisson distribution. A random sample of 100 products contains a total of 11 nonconformities. Do Hypothesis test for Lambda equal 15% at Alpha 1%?

Suppose that two independent random samples of 100, 120 are taken from production line 1 & 2, respectively. Also, Let’s 10, and 12 represents the number of nonconformities in the samples. Develop a procedure for testing the hypothesis that fraction of nonconforming production for both lines (P1, P2) by Normal Distribution approximation. (Alpha=5%)