The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected toaging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to ACvoltage. The values of the parameters depend on the voltage and temperature; suppose α = 2.8 and ß = 220.(a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round youranswers to five decimal places.)at most 250less than 250more than 3000.751980.751980.10648XXXX(b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimalplaces.)0.63119(c) What value (in hr) is such that exactly 50% of all specimens have lifetimes exceeding that value? (Round your answerto three decimal places.)191.074x hr

Answered: Image /qna-images/answer/78b1b1bc-42ed-4cdc-95b9-ce7bc44c27c3.jpg

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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The random variable X is exponentially distributed, where X represents the waiting time to see a shooting star during a meteor shower. If X has an average value of 45 seconds, what are the parameters of the exponential distribution?
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The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 54 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are µ = 28.29 and o = 33.493, respectively. Let X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is x. Use the central limit theorem (CLT) to determine the probability P that the mean taxable wages in James' sample of 54 counties will be less than $31…
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True or False? Assume the below life table was constructed from following individuals who were diagnosed with slow-progressing form of prostate cancer and decided not to receive treatment of any form. The calculated survival probability for year 3, if the Kaplan-Meir approach is used to calculate the survival probability, is approximately 0.85. 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
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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=402 numerical entries from the file and r=107 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 a=.01. Are the data statistically significant at the significance level? Based on your answers, will you reject or fail to reject the null hypothesis?
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Question 1 A population of values has a normal distribution with μ = 143.4 and o= 68.3. You intend to draw a random sample of size n = 164. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is less than 145. P(X < 145) = Find the probability that a sample of size n = P(x < 145) = 164 is randomly selected with a mean less than 145.
You are studying an asset whose price changes each month. You are given n indepen- dent, random observations of the percentage change of an asset over a month (for example, 1%, -2.4%,...). Call this data X1,. mean you call µ and variance 0.1. Call X =;E=1 X;. .., Xn. You find it is Normally distributed, with some n You are interested the average return after 2 independent months if someone invested 1000 dollars, or 0 = E(1000(1+ X;)(1+X;)). Consider the estimate ô = 1000(1+ X)². (a) Find the expected value of 1000(1+ X;)(1+ X;) for any i +j in terms of (b) Is ô an unbiased estimate of 0? What does this mean in practice? (c) What does 0 go to as n gets large using the law of large numbers and other results from class? What does this mean in practice?

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