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?