Understanding Normal Distribution and Calculating Probability for Safe Sailing

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SUMMARY

This discussion focuses on calculating the probability of Mary and Jon safely sailing home based on their weights and the weight limits of their raft. Mary’s weight follows a normal distribution N(68kg, (18)^2 kg) and Jon’s weight follows N(82kg, (15)^2 kg). The total weight of Mary, Jon, and their equipment must not exceed 170kg for them to avoid sinking. The calculation involves combining their weights using the formula for the sum of independent normal distributions.

PREREQUISITES
  • Understanding of normal distribution and its parameters (mean and variance)
  • Familiarity with probability theory and calculations
  • Knowledge of statistical notation and formulas for combining distributions
  • Basic understanding of weight and measurement units in statistics
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  • Learn how to calculate probabilities using the normal distribution
  • Study the properties of independent random variables in statistics
  • Explore the application of the Central Limit Theorem in real-world scenarios
  • Investigate statistical software tools for performing probability calculations, such as R or Python's SciPy library
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Statisticians, data analysts, and anyone involved in probability calculations related to weight and safety assessments in marine activities.

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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