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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 $500\phantom{\rule{0.167em}{0ex}}\text{g}$ and a standard deviation of $15\phantom{\rule{0.167em}{0ex}}\text{g}$. The weights of the candle stands have a mean of $200\phantom{\rule{0.167em}{0ex}}\text{g}$ and a standard deviation of $8\phantom{\rule{0.167em}{0ex}}\text{g}$. 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 $717\phantom{\rule{0.167em}{0ex}}\text{g}$, the company has to pay for additional shipping.
Find the probability that the total weight exceeds $717\phantom{\rule{0.167em}{0ex}}\text{g}$.
$P\left(T>717\right)\approx$