1. A ski gondola that carries skiers to the top of a mountain has a sign stating the maximum capacity is 12 people, or 2100 pounds. That capacity will be exceeded if 12 people have weights with a mean greater than 2100 - 12 = 175 pounds. Since men tend to weigh more than women, then a "worst case" scenario involves 12 passengers who are all men. Suppose that the weights of men have a normal distribution with a mean of 189 pounds and standard deviation of 39 pounds. a) Find the probability that if an individual man is randomly selected, his weight will be greater than 175 pounds. Use a labelled probability density diagram and proper probability notation as part of your solution. b) Find the probability that if 12 men are randomly selected, their mean weight will be greater than 175 pounds. In this case, the gondola will be overloaded! Is this a "likely" occurrence? Explain by interpreting your probability. Use a labelled probability density diagram and proper probability notation as part of your solution. c) Give a reason why passenger safety is likely not a problem for this resort despite your answer to part b)