3. The level of impurity (in percent) in the product of a certain chemical process is a random variablewith probability density function364-x²(4 - x)00 < x < 4otherwisea. What is the probability that the impurity level is greater than 3%?b. What is the probability that the impurity level is between 2% and 3%?c. Find the mean impurity level.d. Find the variance of the impurity levels.

3. Given that, The level of impurity (in percent) in the product of a certain chemical process is a…

Answered: 3. The level of impurity (in percent)…

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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1. Rate data often follow a lognormal distribution. Average power usage (dB per hour) for a particular company is studied and is known to have a lognormal distribution with parameters μ = 4 and σ = 2. a. What is the probability that the company uses more than 270 dB during any particular hour? b. What is the mean power usage (average dB per hour)? What is the variance?
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12. i. State Central limit theorem and tell what is the main theme of it. ii. Show that if the random variables (X, Y) follow the probability density of a bivariate normal distribution and if the correlation p = 0, X and Y are independent. (Show that f(x, y) = g(x) h(y))
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 94 87 83 104 98 108 84 89 The sample mean is x = 93.4. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that o = 12.5. The mean glucose level for horses should be u = 85 mg/100 ml.t Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 85; H,: u + 85; two-tailed O Ho: H = 85; H: µ > 85; right-tailed O Ho: H > 85; H,: µ = 85; right-tailed O Ho: H = 85; H,: µ < 85; left-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The Student's t, since we assume…
Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 88 80 107 97 112 83 87 The sample mean is x ≈ 93.6. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that σ = 12.5. The mean glucose level for horses should be μ = 85 mg/100 ml.† Use α = 0.05. Find (or estimate) the P-value. (Round your answer to four decimal places.)
A1
10. The probability distribution of X, the number of imperfections per 15 meters of a synthetic fabric in continuous rolls of uniform width 2 4 6 8. 10 12 f(x) 0.37 0.35 0.10 0.11 0.01 0.06 Find the average number of imperfections (Mean) and Variance per 15 meter of this fabric
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Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml). 95 86 80 103 99 110 82 87 The sample mean is x = 92.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that o = 12.5. The mean glucose level for horses should be u = 85 mg/100 ml.t Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 85; H,: µ + 85; two-tailed O Ho: H = 85; H,: µ > 85; right-tailed O Ho: H = 85; H,: u 85; H,: u = 85; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal…
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3. We are throwing a die twice. Find the distribution of the random variable |X – Y|= (difference of scored points). Find its mean value and variation. [Ans. E(|X – Y|) = 1,94 ]
d.Find the correlation coefficient between x and y. Show your calculations.e.Comment on the direction and the strength of the association between x and yf. Find the mean value of (x– y) and the standard deviation of (x – y). Show your calculations.

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