Math 370X - Quiz 6Saumil PadhyaOctober 20, 2016Name Net ID1.A motorist just had an accident. The accident is minor with probability 0.75 and is otherwisemajor. Let b be a positive constant. If the accident is minor, then the loss amount follows auniform distribution on the interval [0, b]. If the accident is major, then the loss amountfollows a uniform distribution on the interval [b, 3b]. The median loss amount due to thisaccident is 672. Calculate the mean loss amount due to this accident.(Hint: Let X and Y be 2 random variables which follow a continuous uniform distribution. E[X]= Median(X) and E[Y] = Median(Y). E[X+Y] 6= Median(X+Y)!)(A) 392(B) 512(C) 672(D) 882(E) 10082.The annual profit of a life insurance company is normally distributed. The probability thatthe annual profit does not exceed 2000 is 0.7642. The probability that the annual profit doesnot exceed 3000 is 0.9066. Calculate the probability that the annual profit does not exceed1000.(A) 0.1424(B) 0.3022(C) 0.5478(D) 0.6218(E) 0.725713.Two instruments are used to measure the height, h, of a tower. The error made by the lessaccurate instrument is normally distributed with mean 0 and standard deviation 0.0056h.The error made by the more accurate instrument is normally distributed with mean 0 andstandard deviation 0.0044h. Assuming the two measurements are independent randomvariables, what is the probability that their average value is within 0.005h of the height ofthe tower?(A) 0.38(B) 0.47(C) 0.68(D) 0.84(E) 0.904.The lifetime of a machine part is exponentially distributed with a mean of five years. Calculatethe mean lifetime of the part, given that it survives less than ten years.Hint:f(X|X < a) =f(x)P (X < a)E[X|X < a] =aZ−∞x · f(x|x < a) dx(A) 0.865(B) 1.157(C) 2.568(D) 2.970(E) 3.43525.A certain town experiences an average of 5 tornadoes in any four year period. The numberof years from now until the town experiences its next tornado as well as the number of yearsbetween tornados have identical exponential distributions and all such times are mutuallyindependent Calculate the median number of years from now until the town experiences itsnext tornado.(A) 0.55(B) 0.73(C) 0.80(D) 0.87(E)
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