A water taxi carries passengers from one harbor to another. Assume that the weights of passengers are normally distributed with a mean of 188 lb and a standard deviation of 38lb. The water taxi has a stated capacity of

25 passengers and the water taxi was rated for a load limit of 3500 lb.

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

The maximum mean weight is______

b. If the water taxi is filled with 25 randomly selected passengers, 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 25 passengers and the water taxi is filled with 20 randomly selected passengers, 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 exceed3500 lb?

The probability is _____

d. Is the new capacity of 25 Are passengers safe?

Since the probability of overloading is ____ the new capacity ______ is safe enough.