We have 3 spare transformers supporting 50 single-bank stations. If the failure rate of atransformer in service is 0.05 per year, what is the probability of having no sparesavailable in a year?

A discrete random variable X is said to follow Poisson distribution with parameter λ, if its…

Answered: We have 3 spare transformers supporting…

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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The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 19.1% daily failure rate. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 19.1% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? -(Round to three decimal places as needed.) b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? -(Round to five decimal places as needed.) c. What is the probability of not being awakened if the student uses three independent alarm clocks? -(Round to five decimal places as needed.) d. Do the second and third alarm clocks result in greatly improved reliability? A.Yes, because you can always be certain that at least one alarm clock will work. B.No, because the malfunction of both is equally or more likely than the malfunction of one. C.Yes, because…
4.
A stock index consists of businesses in both Europe and the United States. Assume that each business comprising the stock index makes a profit or loss independently of the other businesses in the index. Suppose that an American business on the stock index makes a profit 60%60% of the time and a European business makes a profit 80%80% of the time. If there are 840 American businesses and 720 European businesses in the stock index, what is the expected number of businesses in the stock index to make a profit?
5. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 2 using the Kaplan-Meir approach and interpret the results. Time in Years Number at Risk, Nt Number of Deaths, Dt Number Censored, Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85. The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study. The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment. The probability of surviving 2 years after…
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 5.6% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? c. What is the probability of not being awakened if the student uses three independent alarm clocks? d. Do the second and third alarm clocks result in greatly improved reliability? A. No, because the malfunction of both is equally or more likely than the malfunction of one. B. No, because total malfunction would still not be unlikely. C. Yes, because total malfunction would not be impossible, but it would be unlikely. D. Yes, because you can always be certain that at…
You may need to use the appropriate appendix table or technology to answer this question. The probability of a plane crashing on a single trip in 2010 was 0.00000276. Find the approximate probability that in 10 million flights, there will be fewer than 37 crashes. (Round your answer to four decimal places.)
2) A data packet consists of 10,000 bits, where each bit is a 0 or a 1 with equal probability. Estimate the probability of having at least 5200 ones in terms of the Q-function. Show your work.
10. An atom of Uranium-238 is unstable and will eventually decay (i.e., emit a particle and turn into a different element). Given an atom of Uranium-238, the time elapsed until it decays, in years, is modeled as an Exponential random variable with parameter 1 = 0.000000000155. How many years must pass for there to be a 50% chance that the Uranium atom decays?

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We have 3 spare transformers supporting 50 single-bank stations. If the failure rate of a transformer in service is 0.05 per year, what is the probability of having no spares available in a year?