Question

A machine which manufactures black polythene dustbin bags, is known to produce 3% defective bags. Following a major breakdown of the machine, extensive repair work is carried out which may result in a change in the percentage of defective bags produced. To investigate this possibility, a random sample of 200 bags is taken from the machine’s production and a count reveals 12 defective bags. What may be concluded?

Here n = 200, p = population proportion of defective bags produced, and it is required to test.

H₀: p = 0.03 (no change)

H_i: p ≠ 0.03 (change; two-tailed)

Significance level, α = 0.05

Again, a Poisson distribution with λ = np provides an approximation to a binomial distribution when n ≥ 50 and p ≤ 0.1 (or p ≥ 0.9)

Thus, if X denotes the number of the defective bags in the sample, then under H₀

  X ~ Po(λ = 200 x 0.03 = 6.0)

Using tables of the Cumulative Poisson Distribution Functions, P(X ≥ 12 = ___________)

Answer 1

Here I am giving you the cumulative probabilities of Poisson distribution.

From this table we get - P( x<= 11) = 0.980

Hope this will help you. Thank you :)