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Sampling for defectives from large lots of manufactured
Chapter 3, Problem 181SE(choose chapter or problem)
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.
Questions & Answers
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,
- , (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,