Suppose that the random variable X has the continuous uniform distribution[1,0 ≤ x ≤ 1Suppose that a random sample of n = 15 observations is selected from this distribution. What is the approximate probabilitydistribution of X - 6? Find the mean and variance of this quantity.Note: Answer can be input as a fraction.Normalf(x) =distribution with mean =and variance =

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Answered: Suppose that the random variable X has…

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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Let x represent the dollar amount spend on supermarket impulse buying in a 10-minute unplanned shopping interval. The mean of this distribution is µ=$25 and the standard deviation is =$10. If we assume the x distribution is approximately normal: (1) What is the probability that a randomly selected shopper will spend between $18 and $22? (1) Consider a random sample of n = 100 shoppers. What is the probability that is between $18 and $22? (2) State two different ways we know the distribution from part (b) is normally distributed.
Assume that we have two normal distributions both with means 0 and standard deviations σ1 and σ2. If σ1 ≥ σ2, then which of P (0 ≤ x ≤ σ1) and P (0 ≤ x ≤ σ2) is bigger? Explain your answer.
Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)
Let X be a normally distributed random variable with a mean of 12 and a standard deviation of 1.25. What proportion of the values of X are less than 14? 0.945 0.933 0.625 None of these choices
Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
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Which of the following statement is INCORRECT? If Y, follows the standard normal distribution and Y, follows a chis-square distribution with degrees of freedom n, then nY/Y t distribution. If X1,.., Xn is a random sample from a normal population with population mean 1 and variance 1, then (X -1) + (X - 1 (X, - 1) follows a chi-square distribution with degrees of freedom n. If X,..., Xn is a random sample from a normal distribution with population mean 0 and a known variance o, then must follow a distribution, where X denotes the sample mean and S denotes the sample standard deviation. If T follows at distribution with degrees of freedom n, then T must follow an F distribution with degrees of freedom 1 and n.
Assume that females have pulse rates that are normally distributed with a mean of μ=74.0 beats per minute and a standard deviation of σ=12.5 beats per minute. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 77 beats per minute. The probability is____

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