The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model fortime (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose a = 2.2 andB = 220.(a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to five decimal places.)at most 2500.73412less than 2500.73412more than 3000.13703(b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.)0.5723(c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answer to three decimal places.)186.242x hr

Let us denote the random variable X as the specimen's lifetime and given that X follows the Weibull…

Answered: The Weibull distribution is widely used…

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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Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch.) (a) At what psi ill the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is (Click to select) v psi. (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) Probability (c) The manufacturer's recommended correct inflation range is 27 psi to 31 psi. Assume the tires' average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire's inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.) Probability
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QUESTION 4 The time to failure of a typical household refrigerator has the following PDF Jo.000192t2 for 0sts 25 yr f(t) elsewhere Find: a. R(15) b. Construct the hazard rate function c. What is the probability that a failure will occur between the second and the tenth year? d. What is the MTTF? Attach File Browse Local Files Browse Content Collection
Product failure behavior. An article in Hotwire (Dec. 2002) discussed the length of time till failure of a product pro- duced at Hewlett-Packard. At the end of the product’s life- time, the time till failure is modeled using an exponential distribution with mean 500 thousand hours. In reliability jargon, this is known as the “wear-out” distribution for the product. During its normal (useful) life, assume the prod- uct’s time till failure is uniformly distributed over the range 100 thousand to 1 million hours. a. At the end of the product’s lifetime, find the probability that the product fails before 700 thousand hours. b. During its normal (useful) life, find the probability that the product fails before 700 thousand hours. c. Show that the probability of the product failing before 830 thousand hours is approximately the same for both the normal (useful) life distribution and the wear-out distribution
Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is (Click to select) : psi. (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) Probability (c) The manufacturer's recommended correct inflation range is 30 psi to 34 psi. Assume the tires' average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire's inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.) Probability
An article suggests the lognormal distribution as a model for SO2 concentration above a certain forest. Suppose the parameter values are μ = 1.7 and σ = 1.2. (a) What are the mean value and standard deviation of concentration? (Round your answers to three decimal places.) (b) What is the probability that concentration is at most 10? Between 5 and 10?
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Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 28 psi (pounds per square inch.) (a) At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is (Click to select): psi. (b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.) Probability (c) The manufacturer's recommended caorrect inflation range is 26 psi to 30 psi. Assume the tires' average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire's inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.) Probability
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…

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