A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 194 lb and a standard...

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A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 194 lb and a standard deviation of 43lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 lb. Complete parts(a) through(d) below.

a.Given that the gondola is rated for a load limit of

3750 lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of

25passengers? The maximum mean weight is lb.

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

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 187.5 lb, which is the maximum mean weight that does not cause the total load to exceed 3750 lb?

The probability is

d.Is the new capacity of 20

passengerssafe?Since the probability of overloading is

under 5 % comma under5%,

over 50 % comma over50%,

the new capacity

appears appears

does not appear doesnotappear

to be safe enough.