Sampling for defectives from large lots of manufactured

Chapter 3, Problem 181SE

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QUESTION:

Problem 181SE

Sampling for defectives from large lots of manufactured product yields a number of defectives, Y , that follows a binomial probability distribution. A sampling plan consists of specifying the number of items n to be included in a sample and an acceptance number a. The lot is accepted if Y a and rejected if Y > a. Let p denote the proportion of defectives in the lot. For n = 5 and a = 0, calculate the probability of lot acceptance if (a) p = 0, (b) p = .1, (c) p = .3, (d) p = .5, (e) p = 1.0. A graph showing the probability of lot acceptance as a function of lot fraction defective is called the operating characteristic curve for the sample plan. Construct the operating characteristic curve for the plan n = 5, a = 0. Notice that a sampling plan is an example of statistical inference. Accepting or rejecting a lot based on information contained in the sample is equivalent to concluding that the lot is either good or bad. “Good” implies that a low fraction is defective and that the lot is therefore suitable for shipment.

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QUESTION:

Problem 181SE

Sampling for defectives from large lots of manufactured product yields a number of defectives, Y , that follows a binomial probability distribution. A sampling plan consists of specifying the number of items n to be included in a sample and an acceptance number a. The lot is accepted if Y a and rejected if Y > a. Let p denote the proportion of defectives in the lot. For n = 5 and a = 0, calculate the probability of lot acceptance if (a) p = 0, (b) p = .1, (c) p = .3, (d) p = .5, (e) p = 1.0. A graph showing the probability of lot acceptance as a function of lot fraction defective is called the operating characteristic curve for the sample plan. Construct the operating characteristic curve for the plan n = 5, a = 0. Notice that a sampling plan is an example of statistical inference. Accepting or rejecting a lot based on information contained in the sample is equivalent to concluding that the lot is either good or bad. “Good” implies that a low fraction is defective and that the lot is therefore suitable for shipment.

ANSWER:

Answer:

Step 1 of 1:

Sampling for the defective product from a lot of manufactured product yields a number of defectives  that follows a binomial distribution.

A sampling plan consists of specifying the number of items  to be included in a sample and an acceptance number .

The lot is accepted if  and rejected if

Let  denote the proportion of defectives in the lot.

For  and  calculate the probability of lot acceptance if,

  1. , (b) , (c) , (d)  (e)

A random variable  is said to have a binomial probability distribution based on  trials with success probability  if and only if

………….(1)

Hence,

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