A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 181 lb and a standard deviation of 37 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts (a) through (c) below.

a. Given that the gondola is rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers?

b. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)?

c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the maximum mean weight that does not cause the total load to exceed 3500 lb? (round to 4 decimals as needed)