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QUESTION 3 10 p Suppose x, Y, and C represent the length, width, and perimeter of a flat rectangular sheet metal part. Note that X is a normal random variable having mean 35cm and standard deviation 3 cm, and Y is independent of X and normally distributed with a mean of 15 cm and a standard deviation of 4 cm. What is the probability that the perimeter is between 96 and 105 cm? ( Report answer to three decmal places. Answer must be within 。001 of correct value)
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