Suppose the amount, a, of impurity A in a vat of hot caramel is normally distributed...

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Suppose the amount, a, of impurity A in a vat of hot caramel is normally distributed with mean 21 and standard deviation 4, the amount, b, of impurity B in the vat of hot caramel is normally distributed with mean 12 and standard deviation 3, and the amount, c, of impurity C in the vat of hot caramel is normally distributed with mean 16 and standard deviation 8. a, b, and c are independent of one another. Let X = total impurity be defined by X = a + b + c. Let W = weighted impurity be defined by W 3a + 4b - 2c %3D a) Calculate the expected value of X. b) Calculate the standard deviation of X. c) Calculate the expected value of W. d) Calculate the variance of W. e) If we pick a value k such that the probability that X > k equals .20 then calculate k? f) The hot caramel is considered impure if X > 53. What is the probability the hot caramel is impure? g) What is the probability that X is within one standard deviation of its expected value? h) What is the probability that a is greater than b? i) What is the probability that a, b, and c are all greater than their expected values. i) Add any comment to the text box below Suppose the amount, a, of impurity A in a vat of hot caramel is normally distributed with mean 21 and standard deviation 4, the amount, b, of impurity B in the vat of hot caramel is normally distributed with mean 12 and standard deviation 3, and the amount, c, of impurity C in the vat of hot caramel is normally distributed with mean 16 and standard deviation 8. a, b, and c are independent of one another. Let X = total impurity be defined by X = a + b + c. Let W = weighted impurity be defined by W 3a + 4b - 2c %3D a) Calculate the expected value of X. b) Calculate the standard deviation of X. c) Calculate the expected value of W. d) Calculate the variance of W. e) If we pick a value k such that the probability that X > k equals .20 then calculate k? f) The hot caramel is considered impure if X > 53. What is the probability the hot caramel is impure? g) What is the probability that X is within one standard deviation of its expected value? h) What is the probability that a is greater than b? i) What is the probability that a, b, and c are all greater than their expected values. i) Add any comment to the text box below

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According to quertion aNN21 A buN12 3 As a bC ECX Eabc ... View the full answer