Question

Many companies use a quality control technique called acceptance sampling to monitor incoming shipments of parts, raw materials, and so on. In the electronics industry, component parts are commonly shipped from suppliers in large lots. Inspection of a sample of 40 components can be viewed as the 40 trials of a binomial experiment. The outcome for each component tested (trial) will be that the component is classified as good or defective. Reynolds Electronics accepts a lot from a particular supplier if the defective components in the lot do not exceed 5%. Suppose a random sample of five items from a recent shipment is tested. Assume that 5% of the shipment is defective and this probability do not change from trial to trial (follows a binomial distribution). What is the probability that four or more items in the sample are defective.

Answer 1

This is clearly mentioned that the given situation is an application of BINOMIAL EXPERIMENT.

Here , number of trials ,n = 5 items.

Probability of component being defective i.e probability of success ,p = 5%= 0.05

let X be the number of defective items out of 5 randomly selected items.

Now we need to find P(X>=4).

FORMULA: P(X=x) = ncx. p^x . q^n-x .

here n=5 , X=4, 5 p=0.05, q=1-p = 1-0.05 = 0.95

P(X>=4) = P(X=4) + P(X=5)

=[5c4 . (0.05)^4 . (0.95)^5-4 ]+[5c5 . (0.05)^5 . (0.95)^5-5 ]

= 0.0000296875 + 0.0000003125

= 0.00003 answer.

Hence, probability that 4 or more items of the sample are defective = 0.00003 answer