Understanding Normal Distribution and Calculating Probability for Safe Sailing

In summary, the conversation discusses women's and men's weights in kilograms and the probability of making it home safely while sailing a raft. The weights of Mary and Jon are a percentage of their own weight and the total weight cannot exceed 170kg. The question asks for help in combining standard deviations and provides a formula for calculating the weight distribution.
  • #1
amywilliams99
4
0
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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  • #2
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.
 

FAQ: Understanding Normal Distribution and Calculating Probability for Safe Sailing

What is the normal distribution?

The normal distribution, also known as the Gaussian distribution, is a common probability distribution that is symmetrical and bell-shaped. It is often used in statistics to describe the distribution of a continuous variable, such as height or weight, in a population.

How is the normal distribution calculated?

The normal distribution is defined by two parameters: the mean (μ) and the standard deviation (σ). The formula for calculating the probability density function of the normal distribution is f(x) = (1/σ√2π) * e^(-(x-μ)^2/2σ^2), where e is the base of the natural logarithm.

What is the 68-95-99.7 rule for the normal distribution?

The 68-95-99.7 rule, also known as the empirical rule, states that approximately 68% of the values in a normal distribution fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.

What is the significance of the normal distribution in statistics?

The normal distribution is significant in statistics because it is often used as a model for real-world data. Many natural phenomena, such as human height or IQ scores, follow a normal distribution. It also allows for easier calculations and interpretation of data compared to other distributions.

Can any data set follow a normal distribution?

No, not all data sets follow a normal distribution. Some data sets may follow other types of distributions, such as the Poisson or exponential distribution. It is important to check the shape of the data before assuming it follows a normal distribution.

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