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  • A process is said to be of six-sigma quality if the process mean is at least six standard deviations from the nearest specification. Assume a normally distributed measurement.(a) If a process mean is centered between the upper and lower specifications at a distance of six standard deviations from each, what is the probability that a produ

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    115
  • A random variable X has the discrete uniform distribution show that the moment-generating function of Xis

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    110
  • A random variable X has the geometric distribution g(x; p) = pqx–1 for x = 1, 2, 3 Show that the moment-generating function of X is and then use Mx(t) to find the mean and variance of the geometricdistribution.

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    154
  • A random variable X has the Poisson distribution p(x; μ) = e–μ μ∞/x for x = 0, 1, 2, Show that the moment-generating function of X is using Mx(t), find the mean and variance of the Poisson distribution.

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  • A service facility operates with two service lines. On a randomly selected day, let X be the proportion of time that the first line is in use whereas Y is the proportion of time that the second line is in use. Suppose that the joint probability density function for (A, V) is(a) Compute the probability that neither line is busy more than h

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    114
  • A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of; 3 of the sets. If x is the number of defective sets purchased by the hotel, find the probability distribution of X. Express the results graphically as a probability histogram.

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    313
  • A square inch of carpeting contains 50 carpet fibers. The probability of a damaged fiber is 0.0001. Assume the damaged fibers occur independently. (a) Approximate the probability of one or more damaged fibers in 1 square yard of carpeting. (b) Approximate the probability of four or more damaged fibers in 1 square yard of carpeting.

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    136
  • A supplier ships a lot of 1000 electrical connectors. A sample of 25 is selected at random, without replacement. Assume the lot contains 100 defective connectors.(a) Using a binomial approximation, what is the probability that there are no defective connectors in the sample?(b) Use the normal approximation to answer the result in part (a)

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    149
  • A tobacco company produces blends of tobacco with each blend containing various proportions of Turkish, domestic, and other tobaccos. The proportions of Turkish and domestic in a blend are random variables with joint density function (X = Turkish and Y = domestic)(a) Find the probability that in a given box the Turkish tobacco accounts fo

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  • An airline makes 200 reservations for a flight that holds 185 passengers. The probability that a passenger arrives for the flight is 0.9 and the passengers are assumed to be independent. (a) Approximate the probability that all the passengers that arrive can be seated.(b) Approximate the probability that there are empty seats.(c) Approxim

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