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2. For a certain population, men's weights follow a normal distribution with mean 172 pounds and standard deviation 21 pounds. An elevator has a maximum capacity of 1920 pounds. If 12 men board the elevator, what is the probability that the elevator will be overloaded? Let X represent the weight of a man from this population. a. If the average weight of the 12 men is over pounds per man then the elevator will be overloaded. Show your work: b. Identify the distribution of the sample means for samples of size 12 taken from this population using the notation shown in lecture. c. Sketch the situation, write the probability question mathematically, write your Tl83/84 entry, and round yourfinal numeric answer to 4 decimal places. d. Express the probability in percent form when completing the sentence. If 12 men enter the elevator, there is a the elevator will be overloaded. (You should find it is not wise for 12 men to board this elevator.)