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 n components can be viewed as the n trials of a binomial the experiment. That outcome for each component test (trail) 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 1%, Suppose a random sample of five items from a recent shipment.

1. Assume tat 1% of the shipment is defective. Compute the probability that no items in the sample are defective
2. Assume that 1% of the shipment is defective. Compute the probability that exactly on item in the sample is defective.
3. What is the probability of the observing on or more defective items in the sample if 1% of the shipment is defective?
4. Would you feel comfortable accepting the shipment if one item was found to be defective? Why or why not?

Answer 1

a) Assuming that 1% of the shipment is defective, the probability that none of the five items in the sample are defective is computed here as:
= (1 - 0.01)⁵ = 0.9510

Therefore 0.9510 is the required probability here.

b) Probability that exactly one in the sample is defective is computed here as:
= 5*0.01*(1 - 0.01)⁴ = 0.0480

Therefore 0.0480 is the required probability here.

c) Given that 1% of the sample is defective, probability that one or more is defective is computed here as:
= 1 - Probability that none of the items are defective

= 1 - 0.9510

= 0.0490

Therefore 0.0490 is the required probability here.

d) The probability of 1 or more item being defective is 0.0490 < 0.05, therefore it is an unusual event given that 1% of the shipment is defective. Therefore if one or more item are defective, then we wont accept the the shipment.