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. The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. a. After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 90% confidence interval for the mean assembly time. b. How many workers should be involved in this study in order to have the mean assembly time estimated un to + 15 seconds with 90% confidence?

. The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. a. After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 90% confidence interval for the mean assembly time. b. How many workers should be involved in this study in order to have the mean assembly time estimated un to + 15 seconds with 90% confidence?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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5. The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. a. After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 90% confidence interval for the mean assembly time. b. How many workers should be involved in this study in order to have the mean assembly time estimated up to + 15 seconds with 90% confidence? 6. A new rocket-launching system is being considered for deployment of small, short-range rockets. The existing system has p = 0.8 as the probability of a successful launch. A sample of 40 experimental launches is made with the new system, and 34 are successful. Using 95% confidence, the confidence interval is 0.85 + 0.111. What is the sample size required @ 90% level of confidence? PART II. ESSAY 1. What is the effect of having different levels of confidence in estimation of population mean? 2. Research and make a report of the importance of confidence interval estimations in business decision making and engineering design. End of Exercise 2
Transcribed Image Text:5. The operations manager of a large production plant would like to estimate the mean amount of time a worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes. a. After observing 120 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 90% confidence interval for the mean assembly time. b. How many workers should be involved in this study in order to have the mean assembly time estimated up to + 15 seconds with 90% confidence? 6. A new rocket-launching system is being considered for deployment of small, short-range rockets. The existing system has p = 0.8 as the probability of a successful launch. A sample of 40 experimental launches is made with the new system, and 34 are successful. Using 95% confidence, the confidence interval is 0.85 + 0.111. What is the sample size required @ 90% level of confidence? PART II. ESSAY 1. What is the effect of having different levels of confidence in estimation of population mean? 2. Research and make a report of the importance of confidence interval estimations in business decision making and engineering design. End of Exercise 2
PART I. CONFIDENCE INTERVAL ESTIMATION 1. The diameter of holes for a cable harness is known to have a normal distribution with a standard deviation of 0.01 inch. A random sample of size 10 yields an average diameter of 1.5045 inch. a. Find a 99% two-sided confidence interval on the mean hole diameter. b. Find a 90% two-sided confidence interval on the mean hole diameter. c. Explain the difference of the interval between the two confidence levels. 2. An article in the Journal of Composite Materials (December 1989, Vol. 23, p. 1200) describes the effect of delamination on the natural frequency of beams made from composite laminates. Five such delaminated beams were subjected to loads, and the resulting frequencies (in hertz) were as follows: 230.66 233.05 232.58 229.48 232.58 a. Calculate a 99% two-sided confidence interval on mean natural frequency. 3. The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, revealing 13 defectives. a. Calculate a 95% two-sided Cl on the fraction of non-defective circuits produced by this particular tool. b. Calculate a 90% upper confidence bound on the fraction of defective circuits. 4. The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidence interval for the standard deviation
Transcribed Image Text:PART I. CONFIDENCE INTERVAL ESTIMATION 1. The diameter of holes for a cable harness is known to have a normal distribution with a standard deviation of 0.01 inch. A random sample of size 10 yields an average diameter of 1.5045 inch. a. Find a 99% two-sided confidence interval on the mean hole diameter. b. Find a 90% two-sided confidence interval on the mean hole diameter. c. Explain the difference of the interval between the two confidence levels. 2. An article in the Journal of Composite Materials (December 1989, Vol. 23, p. 1200) describes the effect of delamination on the natural frequency of beams made from composite laminates. Five such delaminated beams were subjected to loads, and the resulting frequencies (in hertz) were as follows: 230.66 233.05 232.58 229.48 232.58 a. Calculate a 99% two-sided confidence interval on mean natural frequency. 3. The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, revealing 13 defectives. a. Calculate a 95% two-sided Cl on the fraction of non-defective circuits produced by this particular tool. b. Calculate a 90% upper confidence bound on the fraction of defective circuits. 4. The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidence interval for the standard deviation
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