Understanding Normal Distribution and Calculating Probability for Safe Sailing

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The discussion focuses on calculating the probability of Mary and Jon safely sailing their raft without exceeding the weight limit of 170kg. Mary’s weight is normally distributed with a mean of 68kg and a variance of 18^2 kg, while Jon's weight has a mean of 82kg and a variance of 15^2 kg. Their equipment weights are 20% and 50% of their respective weights, which must be factored into the total weight calculation. The formula for combining independent normal distributions is highlighted, emphasizing the need to adjust for the weights of their equipment. Understanding these calculations is crucial for determining the probability of their safe return.
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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