Question: Problem 6.2 A toy consists of three parts whose respective weights (measured in grams) are denoted by X1, X2, X3. Assume that the these weights

Problem 6.2 A toy consists of three parts whose respective weights (measured in grams) are denoted by X1, X2, X3. Assume that the these weights are independent and normally distributed with X1 D = N(150, 36), X2 D = N(100, 25), X3 D = N(250, 60).

(a) Give a formula for the distribution of total weight of the toy T = X1 + X2 + X3; name it and identify the parameters.

(b) What proportion of the toys have weights greater than 520 grams?

(c) Suppose the toys are shipped 24 to a box. The box weighs 200 grams. Calculate the expected value and variance of the total weight of the box.

(d) Describe the distribution of the total weight W of the box; name it and identify the parameters. What is the probability that the total weight of the box is greater than 12,300 grams?

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