Due to rise in average Americans' weight guidelines are provided for airlines, expecting that plane passengers in the coming season will have an average weight of 190 pounds (luggage and clothes, etc, included). Standard deviation is not provided, but 35 pounds would be a reasonable value. Weights are not really normally distributed especially in this case because both men and women are included in the population.

A passenger plane carries 25 passengers. What will be a good distribution model for the weights of the passengers?

What is the mean and variance of the 25 passengers?

What is the probability that the total weight of passengers and their belongings exceeds 5200 pounds?


If you are looking at such a question, with no distribution, I'd suggest you take a look at the Markov's inequality or Chebyshev's inequality to solve your question. Unfortunately, your sample size of 25 does not qualify to use Central Limit Theorem to estimate the distribution of the sample...so I'd say the above 2 are the better ones..at least my gut tells me so.

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  • $\begingroup$ Is it possible to be uniform? I learned Chebyshev's somewhere else but it's not covered in this class yet. The probability distributions that are covered thus far are normal, uniform, and exponential for continuous variables; and uniform, geometric, binomial, and Bernoulli for discrete variables. I'm pretty sure that weight is continuous. Given the small sample size, is it possible that the distribution is uniform? $\endgroup$ – user60852 Feb 14 '13 at 7:33
  • $\begingroup$ Or exponential? Because the weight of passengers can never be negative? $\endgroup$ – user60852 Feb 14 '13 at 7:57
  • $\begingroup$ consider re-writing your question again because we really do not have sufficient information to suggest a distribution to you. $\endgroup$ – bryanblackbee Feb 14 '13 at 8:06

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