A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 183 lb and a standard deviation of 38 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(d) 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?

The maximum mean weight is lb.

(type an integer or a decimal. Do notround.)

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

The probability is .

(Round to four decimal places asneeded.)

c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selectedskiers, 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?

The probability is .

(Round to four decimal places asneeded.)

d. Is the new capacity of 20 passengerssafe?

Since the probability of overloading is

a. under 5 %

b. over 50%

the new capacity

a. appears

b. does not appear

to be safe enough.