3. Thirteen and ten items produced by two machines, old and new respectively, were selected atrandom and the times taken by the machines to produce the items are listed below:MachineProduction Times (in minutes)ТуреOld41188710876New567431167Assume that the production times are normally distributed,a. Are you 95% confident that the true variations in production times are not different regardless ofthe type of machines used? Justify your answer. [(0.187,2.493), Yes because ..]b. Use your answer in part (a) to construct a 95% confidence interval for the difference in the meanproduction times when the items are produced using old and new machines. Hence, verify if thenew machine is significantly faster that the old machine in producing such items. [(-0.6039,2.8192),Yes because.] The lifetime of 'Ener' and 'Gizer' light bulbs are assumedto be normally distributed. A random sample of 50'Eneilight bulbs and 64 'Gizef light bulbs was tested. Thefollowing results (in hours) were obtained:Ener (X)Gizer (Y)Σx = 128,000y = 127,808E(x- )? = 798720- ) = 9513Find the 95% confidencein tenal for the difierence between the mean lifetime of the two brands oflightbutb. [(558.354,567.646)]

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The records of a light bulb manufacturer show that, when the manufacturing machinery is working correctly, the defect rate (due to imperfections in the material used) is 1%. The manufacturer's control department periodically tests samples of the bulbs, and when 1.25% or more are defective, they call repair technicians for service. The control department is going to take a random sample of 4400 light bulbs. Let p be the proportion of defective light bulbs in the sample assuming the machinery is working correctly. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p. (b) Find the standard deviation of p. (c) Compute an approximation for P(P ≥ 0.0125), which is the probability that, assuming the machinery is working correctly, the repair technicians will be called. Round your answer to four decimal places.
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The lifetime of 'Ener' and 'Gizer' light bulbs are assumed to be normally distributed. A random sample of 50'Enei light bulbs and 64 'Gizef' light bulbs was tested. The following results (in hours) were obtained: