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# Combining normal random variables

You might need: Calculator,Z table

## Problem

A company produces and sells homemade candles and accessories. Their customers commonly order a large candle and a matching candle stand. The weights of these candles have a mean of 500, start text, g, end text and a standard deviation of 15, start text, g, end text. The weights of the candle stands have a mean of 200, start text, g, end text and a standard deviation of 8, start text, g, end text. Both distributions are approximately normal.
Let T, equals the total weight of a randomly selected candle and a randomly selected stand, and assume that the two weights are independent.
If the total weight T of the two items exceeds 717, start text, g, end text, the company has to pay for additional shipping.
Find the probability that the total weight exceeds 717, start text, g, end text.
You may round your answer to two decimal places.
P, left parenthesis, T, is greater than, 717, right parenthesis, approximately equals
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