Question: A certain product is assembled by placing three components end to end. The components lengths are L 1 , L 2 , and L 3

A certain product is assembled by placing three components end to end. The components’ lengths are L₁, L₂, and L₃. Each component is manufactured on a different machine, so the random variations in their lengths are independent of one another. The lengths are normally distributed with means of 1, 2, and 1.5 ft and variances of 0.00014, 0.0002, and 0.0003, respectively.

a. Compute the mean and variance of the length of the assembled product.

b. Estimate the percentage of assembled products that will be no less than 4.48 and no more than 4.52 ft in length.

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