Normal approximation to compute the probability:
A lot contains 100 articles of which 10 are defective. The lot is rejected if a random sample of 10 articles drawn from the lot contains more than 2 defectives. Use normal approximation to compute the probability that the lot is accepted.
Solution:
Let X represents the number of defective articles in the sample. The variable X follows the hypergeometric distribution with parameters
N = 100,n - 10,M = l0 and has E(X) = 10.(10/100) = 1 and
V(X) =σ^{2} = 10.10/100.(1-(10/100)) (100-10/100-1) =9/11
The required probability is