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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 n components can be viewed as the n 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 1%. Suppose a random sample of five items from a recent shipment is tested. a. Assume that 1% of the shipment is defective. Compute the probability that no items in the sample are defective. b. Assume that 1% of the shipment is defective. Compute the probability that exactly one item in the sample is defective. c. What is the probability of observing one or more defective items in the sample if 1% of the shipment is defective? would you feel comfortable accepting the shipment if one item was found to be defective? Why or why not?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 5, Problem 66SE
Textbook Problem
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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 n components can be viewed as the n 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 1%. Suppose a random sample of five items from a recent shipment is tested.

  1. a. Assume that 1% of the shipment is defective. Compute the probability that no items in the sample are defective.
  2. b. Assume that 1% of the shipment is defective. Compute the probability that exactly one item in the sample is defective.
  3. c. What is the probability of observing one or more defective items in the sample if 1% of the shipment is defective?

would you feel comfortable accepting the shipment if one item was found to be defective? Why or why not?

a.

To determine

Find the probability that no items in the sample are defective if 1% of the shipment is defective.

Explanation of Solution

Calculation:

Reynolds Electronics accepts a lot from a particular supplier if the defective components in the lot do not exceed 1%. The two outcomes for the trial are good or defective. The inspection of n components is considered as the n trials of the binomial experiment. A random sample of five items from the recent shipment is tested.

Define the random variable x as the number of items that are defective. Here, a random sample (n) of 5 items from the recent shipment is tested. Each item is independent of the other. Also, there are two possible outcomes, item is good or the item is defective (success or failure). The company accepts a lot from a particular supplier if the defective components in the lot do not exceed 1%. Thus, the probability of success (p) is 0.01. Thus, x follows binomial distribution.

The probability of obtaining x successes in n independent trails of a binomial experiment is,

f(x)=(nx)px(1p)nx,x=0,1,2,...,n

Where, p is the probability of success

b.

To determine

Find the probability that exactly one item in the sample is defective if 1% of the shipment is defective.

c.

To determine

Find the probability that one or more items in the sample are defective if 1% of the shipment is defective.

d.

To determine

Explain whether it is comfortable accepting the shipment if one item was found to be defective.

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Chapter 5 Solutions

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