Example #4A component has the following linear hazard rate, where t is inyears2(t) = 0.4t,t >0%3Da) Find R(t) and determine the probability of a componentfalling within the first month of its operationb) What is the design life if a reliability of .95 is desired?

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Answered: a) Find R(t) and determine the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Gebhardt Electronics Gebhardt Electronics produces a wide variety of transformers that it sells directly to manufacturers of electronics equipment. For one component used in several models of its transformers, Gebhardt uses a 3-foot length of .20 mm diameter solid wire made of pure Oxygen-Free Electronic (OFE) copper. A flaw in the wire reduces its conductivity and increases the likelihood it will break, and this critical component is difficult to reach and repair after a transformer has been constructed. Therefore, Gebhardt wants to use primarily flawless lengths of wire in making this component. The company is willing to accept no more than a l in 20 chance that a 3-foot length taken from a spool will be flawless. Gebhardt also occasionally uses smaller pieces of the same wire in the manufacture of other compo- nents, so the 3-foot segments to be used for this component are essentially taken randomly from a long spool of .20 mm diameter solid OFE copper wire. Gebhardt is now…
A researcher predicts that scores in treatment A will be higher than scores in treatment B. If the mean for the n = 10 participants in treatment A is 4 points higher than the mean for the n = 10 participants in treatment B and the data produce t = 1.985, which decision should be made? a. reject H0 if α = .05 and if α = .01 b. fail to reject H0 if α = .05 and if α = .01 c. fail to reject H0 if α = .05 but reject H0 if α = .01 d. reject H0 if α = .05 but fail to reject H0 if α = .01
You are a researcher who wants to know what the mean (µ) level of anxiety would be for the whole population if they were all receiving a new anti-anxiety therapy. You can’t give the therapy to the whole population, so you give it to a sample, and you get M = 32.1 as the average anxiety level for the sample on the therapy. What is the reason that you can’t just simply assume that µ = 32.1? You didn’t use random assignment Sampling error Descriptive statistics Inferential statistics
Are Republicans less likely than Democrats to display the American flag in front of their residence on the Fourth of July? 409 of the 660 Republicans surveyed display the flag on the Fourth of July and 472 of the 687 Democrats surveyed display the flag on the Fourth of July. What can be concluded at the a = 0.05 level of significance? For this study, we should use Select an answer a. The null and alternative hypotheses would be: Ho: Select an answer v Select an ahswer vSelect an answer v (please enter a decimal) H1: [Select an answer Select an answer v Select an answer v (Please enter a decimal) b. The test statistic ? v (please show your answer to 3 decimal places.) !! c. The p-value (Please show your answer to 4 decimal places.) d. The p-value is ? va e. Based on this, we should Select an answer v the null hypothesis.
The Arrow-Pratt measures of absolute and relative risk aversion respectively describe the willingness of a consumers to risk a fixed amount of wealth or a fixed fraction of their wealth. This problem will demonstrate this by setting up a simple investment problem. Suppose that consumers begin with initial wealth Wo and may buy shares of a risky asset whose payoff per share is given by 2. (1 w/ prob. P, X = 1-1 w/ prob.1– p. Therefore buying { shares of the risky asset yields final wealth W = Wo +X. Suppose that each consumer may buy an unlimited number of shares, and seeks to maximize expected utility of final wealth max E[u(W)]. (a) Expand the consumer's expected utility maximization problem, and find the first order condition. (b) Let Cara be a consumer whose utility function exhibits constant absolute risk aver- sion UA(W) = 1– e-aW Find Cara's optimal number of shares and show that it does not depend on her starting wealth Wo-
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.14 kgf/cm2 for the modified mortar (m 42) and y = 16.89 kgf/cm2 for the unmodified mortar (n 30). Let and be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the %D bond strength distributions are both normal. (a) Assuming that = 1.6 and o, 1.3, test Ho: Hy-H2 O versus H: µ, - µ, > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds from 0. o Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds…

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a) Find R(t) and determine the probability of a component falling within the first month of its operation b) What is the design life if a reliability of .95 is desired?