1. Define the random variable X as the time (in months) a jet engine can operate before needing to be rebuilt. The cumulative distribution function F(x) \((P(X \leq x))\) is given to be:\[F(x) = \begin{cases} 0 & x \leq 0 \\1 - \exp\left(-0.03x^{1.2}\right) = 1 - e^{-0.03x^{1.2}} & x > 0 \end{cases}\]a. What is the probability that a jet engine will last less than 12 months before needing to be rebuilt?b. What is the probability that a jet engine will last more than 12 months before needing to be rebuilt?c. Given a jet engine has lasted more than 6 months, what is the probability it will last more than 12 months before needing a rebuild?d. Find the 50-th percentile of X. That is to say the value of x such that \(P(X \le x) = 0.5\).e. Find the probability density function f(x).

Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART ONLY PLZ REPOST FOR REMAINING PARTS

Answered: a. What is the probability that a jet…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable x. X P(x) 0 0.125 1 0.375 2 0.375 3 0.125 O A. mean: 1.50; standard deviation: 0.87 OB. mean: 1.50; standard deviation: 0.76 O C. mean: 2.25; standard deviation: 0.87 O D. mean: 2.25; standard deviation: 0.76 C
The life of a butterfly is normally distributed with a mean of 50 days. You took a random sample of 25 such butterflies. The mean life for this sample is 47 days a standard deviation of 3 days. At α = 0.05. a. Test to see if the average life of a butterfly is different from 50 days. b. Your friend believes that the life of a butterfly is less than 50 days. Is she correct?
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In a Normal distribution, the Empirical Rule states that... ["", "", "", "", ""] of the data is within 1 standard deviation of the mean, ["", "", "", "", ""] of the data is within 2 standard deviation of the mean, and ["", "", "", "", ""] of the data is within 3 standard deviation of the mean.
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=| S= (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…
The ages of a random sample of motorcyclists when they were fatally injured in traffic crashes were recorded and tabled below: Age (in years) Below 16 1628 28 - < 40 40 - < 52 52 - < 64 64 - <76 B. 0.55 C. 0.44 Frequency 0 2 6 10 13 5 D. 0.50 Midpoints The relative frequency of motorcyclist's aged between 20 and 50 who were fatally injured in traffic crashes is (rounded off to two decimals): A. 0.38 22 34 46 58 70 Cumulative freq. 0 2 8 18 31 36

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