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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?

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,

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.

Step 3

The required proba...

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