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\text { 5. Suppose } X_{1} \sim N\left(\mu_{1}, \sigma_{1}{ }^{2}\right) \text { and } X_{2} \sim N\left(\mu_{2}, \sigma_{2}{ }^{2}\right) \text { where } X_{1}, X_{2} \text { are independent random variables. } (a) What is the distribution of X₁ + X₂? (Be specific about the parameters.) (b) Suppose a product is assembled with two parts: A and B. The weights of part A are normally distributed witha mean of 3 lbs and a standard deviation of 1 lb. The weights of part B are normally distributed with a mean of 1lb and a standard deviation of 1 lb. Suppose we randomly select a completed product from the production line. What is the probability that the weight of the completed product is less than 4.5 lbs? Let X₁ be the weight of part A and X₂ be the weight of part B so that, Y=X_{1}+X_{2} \text { is the weight of the completed product. Find } P(Y<4.5)

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