A particular lift has a maximum load capacity of $$\(700 \mathrm{~kg}\)$$. The weights of men are normally distributed with mean $$\(80 \mathrm{~kg}\)$$ and standard deviation $$\(10 \mathrm{~kg}\)$$. The weights of women are normally distributed with mean $$\(69 \mathrm{~kg}\)$$ and standard deviation $$\(5 \mathrm{~kg}\)$$. You may assume that weights of people are independent. Find the value of $$\(c\)$$ such that the probability of the load exceeding $$\(700 \mathrm{~kg}\)$$ is less than $$\(2.5 \%\)$$ no matter the gender of the occupants. (6)

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