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 is under 683g, the company gets a discount on shipping.
Find the probability that the total weight is under 683g.
You may round your answer to two decimal places.
P(T<683)≈