Understanding Normal Distribution and Calculating Probability for Safe Sailing

amywilliams99
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If anyone could help me with the following Q it would be much appreciated!

Womens weights - N (68kg, (18)^2 kg) Mens Weights - N (82kg, (15)^2 kg)
Mary and Jon are sailing a raft. Marys equipment weights 20% of her weight. Jons weighs 50% of his weight. The raft will sink if the total weight is greater than 170kg.
Compute the probability that they make it home safely. (assume weights of mary and jon are sampled independantly from the relevant distributions?

I am having trouble with how to combine the standard deviations etc. Please help!
 
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If x1 ~ N(m1, s12) and x2 ~ N(m2, s22) then ax1 + bx2 ~ N(am1+bm2, a2s12 + b2s22).

Note, the unit of variance is not kg but kg2.
 

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