Question 4
25 pts
A ski gondola in Vail, CO, carries skiers to the top of a mountain. It bears a plaque stating that
the maximum capacity is 12 people or 2280 pounds. That capacity will be exceeded if 12
people have weights with a mean greater than 2280/12 = 190 pounds. Because men tend to
weigh more than women, a "worst case" scenario involves 12 passengers who are all men.
Men have weights that are normally distributed with a mean (μ) of 182.9 pounds and a
standard deviation (σ) of 40.8 pounds.
Find the probability that one randomly selected man will have a weight greater than 190
pounds. Please state your probability to 4 decimal places.
The probability that one randomly selected man will have a weight greater than 190 pounds is
Find the probability that 12 randomly selected men will have a mean weight that is greater
than 190 pounds (so that their total weight exceeds the maximum of 2280 lb). Please state
your probability to 4 decimal places.
The probability that 12 randomly selected men will have a mean weight that is greater than
190 pounds is
Does the gondola appear to have a feasible weight limit?
Please type yes or no in the blank