A water taxi carries passengers from one harbor to another. Assume that passengers' weights are normally distributed with a mean of 197 lb and a standard deviation of 44 lb. The water taxi has a stated capacity of 25 passengers and was rated for a load limit of 3750 lb.

Given that the water taxi was rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers if it is filled to the stated capacity of 25 passengers?

The maximum mean weight is__________lb. (Type an integer or a decimal. Do not round.)

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________

(Round to four decimal places as needed.)

If the weight assumptions were revised so that the new capacity became

20 passengers and the water taxi is filled with 20 randomly selected passengers, 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_________ (Round to four decimal places as needed.)

Is the new capacity of 20 passengers safe?

Since the probability of overloading is______________

under 5 %, or over 50 %

the new capacity ____________

appears or does not appear

to be safe enough.