A ski gondola in Vail, Colorado, carries skiers on the top of a mountain, It bears a plaque stating that the maximum capacity is 12 people or 2004 lb. That capacity will be exceeded if 12 people have weights with a mean greater the 167 lb. Because men tend to weigh more than women, a worst-case scenario involves 12 passengers who are all men. Assume that weights of men are normally distributed with the mean of 182.9 lb and a standard deviation of 40.8 lb. Required:
a. Find the probability if an individual man is randomlyselected, his weight will be greater than 167lb.
b. Find the probability that 12 randomly selected men willhave a mean that is greater than 167 lbs (so total weught isgreater than 2004 lbs)
c. Does the gondola appear to have the correct weight limit?Why or why not?