Production and Operations Analysis, Seventh Edition
7th Edition
ISBN: 9781478623069
Author: Steven Nahmias, Tava Lennon Olsen
Publisher: Waveland Press, Inc.
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Question
Chapter 12.10, Problem 40P
Summary Introduction
A.
Interpretation: The probability of rejecting the lot on the first sample needs to calculated
Concept Introduction: Double sampling has a psychological advantage over single sampling as it gives second chance to decide the acceptance and rejection of the sample.
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Consider the following double sampling plan. First select a sample of 5 from a lotof 100. If there are four or more defectives in the sample, reject the lot. If there isone or fewer defective, accept the lot. If there are two or three defectives, samplean additional five items and reject the lot if the combined number of defectives inboth samples is five or more. If the lot has 10 defectives, what is the probabilitythat a lot passes the inspection?
For the double sampling plan described in Problem 39, determine the following:b. The probability that the lot is rejected based on the second sample.
Sampling error is defined as:
an error that occurs when a sample of less than 30 elements is drawn.
an error that occurs during collection, recording, and tabulation of data.
the difference between the value of a sample statistic and the value of the corresponding population parameter.
A company employs the following sampling plan: It draws a sample of 10 percentof the lot being inspected. If 1 percent or less of the sample is defective, the lot isaccepted. Otherwise the lot is rejected.b. If a lot contains 1,000 items of which 20 are defective, what is the probabilitythat the lot is accepted?
Chapter 12 Solutions
Production and Operations Analysis, Seventh Edition
Ch. 12.1 - Prob. 2PCh. 12.1 - Prob. 3PCh. 12.1 - Prob. 4PCh. 12.1 - Prob. 5PCh. 12.1 - Prob. 6PCh. 12.2 - Prob. 7PCh. 12.2 - Prob. 8PCh. 12.2 - Prob. 9PCh. 12.2 - Prob. 10PCh. 12.2 - Prob. 11P
Ch. 12.2 - Prob. 12PCh. 12.2 - Prob. 13PCh. 12.3 - Prob. 14PCh. 12.3 - Prob. 15PCh. 12.3 - Prob. 16PCh. 12.3 - Prob. 17PCh. 12.4 - Prob. 18PCh. 12.4 - Prob. 19PCh. 12.4 - Prob. 20PCh. 12.4 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.6 - Prob. 23PCh. 12.6 - Prob. 24PCh. 12.6 - Prob. 25PCh. 12.6 - Prob. 26PCh. 12.6 - Prob. 27PCh. 12.6 - Prob. 28PCh. 12.9 - Prob. 29PCh. 12.9 - Prob. 30PCh. 12.9 - Prob. 31PCh. 12.9 - Prob. 32PCh. 12.9 - Prob. 33PCh. 12.10 - Prob. 34PCh. 12.10 - Prob. 35PCh. 12.10 - Prob. 37PCh. 12.10 - Prob. 38PCh. 12.10 - Prob. 39PCh. 12.10 - Prob. 40PCh. 12.11 - Prob. 41PCh. 12.11 - Prob. 42PCh. 12.11 - Prob. 43PCh. 12.11 - Prob. 44PCh. 12.12 - Prob. 46PCh. 12.12 - Prob. 47PCh. 12.12 - Prob. 48PCh. 12 - Prob. 49APCh. 12 - Prob. 50APCh. 12 - Prob. 51APCh. 12 - Prob. 52APCh. 12 - Prob. 53APCh. 12 - Prob. 54APCh. 12 - Prob. 55APCh. 12 - Prob. 57APCh. 12 - Prob. 58APCh. 12 - Prob. 59APCh. 12 - Prob. 60APCh. 12 - Prob. 61APCh. 12 - Prob. 62APCh. 12 - Prob. 63APCh. 12 - Prob. 64APCh. 12 - Prob. 65APCh. 12 - Prob. 66APCh. 12 - Prob. 67APCh. 12 - Prob. 68APCh. 12 - Prob. 69APCh. 12 - Prob. 70AP
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- A single sampling inspection scheme for large lot of mass-produced flanges states:From each lot take and inspect a random sample of 50. If 3 or more defectives, inspect the whole lot and remove all defectives, if less than 3 are found accept the lot without further inspection.a. Obtain the equation for Pa the probability that a lot containing a fraction p of defectives will be accepted, in terms of p.b. Evaluate Pa for p=0.01, 0.02, 0.03, 0.05, 0.07, 0.10, 0.15, 0.20, 0.30. Plotthe operating characteristics and average outgoing quality curve.c. Estimate: (a) the producer’s Risk at p of 2% (b) the consumer’s Risk for pof 5%.arrow_forwardA company employs the following sampling plan: It draws a sample of 10 percentof the lot being inspected. If 1 percent or less of the sample is defective, the lot isaccepted. Otherwise the lot is rejected. c. If a lot contains 10,000 items of which 200 are defective, what is the probability that the lot is accepted?arrow_forwardThe director of research and development is testing a new drug. She wants to know if there is evidence at the 0.02 level that the drug stays in the system for less than 368 minutes. For a sample of 78 patients, the mean time the drug stayed in the system was 363 minutes. Assume the variance is known to be 529. State the null and alternative hypotheses for the above scenario.arrow_forward
- The general meaning of a standard error is best described by which of the following? a. A standard error is another term for the estimated standard deviation of the population. b. If you go out about two standard errors on either side of 0, you can be about 95% confident that the unknown population parameter will be in the resulting interval. c. A standard error is essentially a standard deviation, specifically, the standard deviation of the sampling distribution of the estimate of the population parameter. d. All of these choices are correct characterizations of a typical standard error.arrow_forwardAn industrial process that makes 3-foot sections of plasticpipe produces pipe with an average inside diameter of 1 inch and a standard deviation of .05 inch.a. If you randomly select one piece of pipe, what is the probability that its inside diameter willexceed 1.02 inches, assuming the population is normal?b. If you select a random sample of 25 pieces of pipe, what is the probability that the sample meanwill exceed 1.02 inches?μ = 1.00, σ = .05arrow_forwardWhen samples of size n are drawn from a population, then the sampling distribution of the sample mean X is approximately normal, provided that n is reasonably large. a. True b. Falsearrow_forward
- Since each process capability index relies on the estimate of process standard deviation, which in turns relies on sampling, therefore which following statement is INCORRECT? a. Confidence interval of each capability index should be found, instead of computing only a point estimate. b. Each process capability index follows some distribution. c. Each process capability index is a random variable. d. The distribution of Cpk is approximately normal. e. none of the abovearrow_forwardThe Empirical Rule tells us that … a) __________ of the data lies within 1 standard deviation of the mean b) __________ of the data lies within 2 standard deviation of the mean c) __________ of the data lies within 3 standard deviation of the meanarrow_forwardIf n is large and the population standard deviation is unknown, the standard error of the sampling distribution of the sample mean is equal to: the sample standard deviation divided by the sample size. the population standard deviation multiplied by the sample size. the sample standard deviation divided by the square root of the sample size.arrow_forward
- The standard error of the sampling distribution of the sample mean for a sample size of n drawn from a population with a mean of μ and a standard deviation of σ is: sample standard deviation divided by the sample size. sample standard deviation divided by the square root of the sample size. population standard deviation divided by the square root of the sample size.arrow_forwardThe Central Limit Theorem guarantees an approximately normal sampling distribution when n is sufficiently large. A- true B- falsearrow_forwardA carpenter is making doors that are 2058 millimeters tall. If the doors are too long they must be trimmed, and if they are too short they cannot be used. A sample of 13 doors is made, and it is found that they have a mean of 2043 millimeters with a variance of 1024. Is there evidence at the 0.025 level that the doors are too short and unusable? State the null and alternative hypotheses for the above scenario.arrow_forward
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