Question: 5.) Suppose that X is a normal random variable with mean and standard deviation: Hx = 15, ox= 1.2. Suppose also that Y is

5.) Suppose that X is a normal random variable with mean and standard deviation: Hx = 15, ox= 1.2. Suppose also that Y is also a normal random variable with mean and standard deviation: Hy = 25, y = 2.5. Now suppose that the random variable W is their sum: W = X+Y. a.) What condition is required to assure that Wis also a normal random variable? Answer: b.) Assuming this condition is true, what then are the mean and standard deviation of W? Hw= I Ow= = c.) Find the probability: P(X 16.0) = = Page 3

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