Acceptance Sampling. Exercises 35 and 36 involve the method of acceptance sampling, whereby a shipment of a large number of items is accepted based on test results from a sample of the items.AAA batteries AAA batteries are made by companies including Duracell, Energizer, Eveready, and Panasonic. When purchasing bulk orders of AAA batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select 50 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 2000 AAA batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?

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Asked Jan 9, 2020
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Acceptance Sampling. Exercises 35 and 36 involve the method of acceptance sampling, whereby a shipment of a large number of items is accepted based on test results from a sample of the items.

AAA batteries AAA batteries are made by companies including Duracell, Energizer, Eveready, and Panasonic. When purchasing bulk orders of AAA batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select 50 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 2000 AAA batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?

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Expert Answer

Step 1

Define the random variable x, as the number of defective batteries. The probability of defects in a shipment is 0.02, and there are two possible outcomes (accepted and rejected). Also, each shipment is independent of the other. Hence, x follows binomial distribution.

The formula for the binomial distribution is,

Statistics homework question answer, step 1, image 1
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Step 2

Where, n is the number of trials, x is the number of successes among n trials, p is the probability of success and q is the probability of failure.

Since, the shipment will be accepted if there are 2 or less defectives, x takes the values as 0, 1 and 2.

Statistics homework question answer, step 2, image 1
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Step 3

The required proba...

Statistics homework question answer, step 3, image 1
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