The lifetime, in drilling hours, of a particular type of drill bit is wellmodelled by a Weibull distribution with parameters a = 2.1 and B=3.6(c)(i)Calculate the probability that the lifetime of a randomly chosendrill bit is between 4 hours and 5 hours.(ii)Calculate the mean and standard deviation of the drill bit lifetime.

Weibull distribution is a continuous type distribution. It may be of one parameter, two parameters,…

Answered: The lifetime, in drilling hours, of a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose the longevity of iPad batteries, X, can be modeled by a normal distribution with mean μ = 8.2 hours and standard deviation σ = 1.2 hours, i.e. X ∼ N (μ = 8.2, σ = 1.2). (a) Find the probability a randomly selected iPad lasts less than 10 hours. (b) Suppose 16 iPads are randomly selected. Find the probability that the mean longevity, X ̄, is less than 7.9 hours. (c) Find the 25th percentile of the individual battery times, X. (d) Suppose 16 iPads are randomly selected. Find the 25th percentile of the sample mean X ̄. (e) Suppose 16 iPads are randomly selected. Let Y equal the number with longevity more than 10 hours. What is the distribution of Y ? (f) In reference to question 6.5(e), determine the probability that exactly 2 of the iPads last longer than 10 hours.
Assume that adults have IQ scores that are normally distributed with a mean of μ=100and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 128.
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Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 124 The probability that a randomly selected adult has an IQ less than 124 is (Type an integer or decimal rounded to four decimal places as needed.)
Rosie is an aging sheepdog in Montana who gets regular checkups from her owner, the local veterinarian. Let x be a random variable that represents Rosie’s resting heart rate (in beats per minute). From past experience, the vet knows that x has a normal distribution with σ= 12. The vet checked the manual and found that for dogs of this breed, μ= 115beats per minute. Over the past six weeks(n=6), Rosie’s sample mean hear rate was x̄=105.0. The vet is concerned that Rosie’s heart rate is slowing and is less than 115.0. Does the data indicate that this is the case? Use a level of significance α= .05 to conduct a hypothesis test. You must include the following: i) null hypothesis ii) alternate hypothesis iii) test statistic (z or t value –remember the information in the problem will help determine if you use a z or t) iv) P-Value compared to the level of significance(α). v) Conclusion (Do you reject or fail to reject the vet’s claim?)
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Assume that adults have IQ scores that are normally distributed with a mean of mμ=100 and a standard deviation σ= 15. Find the probability that a randomly selected adult has an IQ less than 127. The probability that a randomly selected adult has an IQ less tha 127 is
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Using the accompanying table of data, blood platelet counts of women have a bell-shaped distribution with a mean of 254.9 and a standard deviation of 65.3. (All units are 1000cells/muL.) Using Chebyshev's theorem, what is known about the percentage of women with platelet counts that are within 2 standard deviations of the mean? What are the minimum and maximum possible platelet counts that are within 2 standard deviations of the mean? 321297287262216249387217500348330188244250186391193234231216222168335241275253573157186246394217237199201204227219182252316212242172314338246213240225375234227307308228370186241288227178263330184184292228288239216263206184246310254236207266224212255169359167321171295270164167378219283341242223256260230387240234233271263248275281334244330297203195175333210227263257282233222257220183323261209231250206239255302275394180308231189237132243291

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