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Combining normal random variables

You might need: Calculator,Z table


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 500g and a standard deviation of 15g. The weights of the candle stands have a mean of 200g and a standard deviation of 8g. Both distributions are approximately normal.
Let T= 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 717g, the company has to pay for additional shipping.
Find the probability that the total weight exceeds 717g.
You may round your answer to two decimal places.
  • Your answer should be
  • an exact decimal, like 0.75