Light Bulb Problem: Light bulb manufacturers like to be assured that their bulbs will

Chapter 9, Problem 29

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Light Bulb Problem: Light bulb manufacturers like to be assured that their bulbs will work. Because testing every bulb is impractical, a random sample of bulbs is tested. Suppose that the quality control department at a light bulb factory decides to test a random sample of 5 bulbs for every 100 that are made. a. In how many different ways could a 5-bulb sample be taken from 100 bulbs? b. To check the quality control process, the manager of the factory puts 2 defective bulbs in with 98 working bulbs before the sample is taken. How many different ways could a sample of 5 of these 100 bulbs be selected that contains at least 1 of the defective bulbs? c. If the 100 bulbs include 2 defective bulbs, what is the probability that the sampling process will reveal at least 1 defective bulb? d. Based on your answers, do you think that the 5-bulb-in-100 sampling plan is sufficiently effective?