A boat capsized and sank in a lake. Based on an assumption of a mean weight of143

lb, the boat was rated to carry50 passengers(so the load limit was7,150lb). After the boatsank, the assumed mean weight for similar boats was changed from143 lb to170 lb. Complete parts a and b below.

a.Assume that a similar boat is loaded with50passengers, and assume that the weights of people are normally distributed with a mean of179.9 lb and a standard deviation of36.8 lb. Find the probability that the boat is overloaded because the50 passengers have a mean weight greater than143 lb.

The probability is

enter your response here.

(Round to four decimal places asneeded.)

b. The boat was later rated to carry only16passengers, and the load limit was changed to

2,720 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than170(so that their total weight is greater than the maximum capacity of2,720lb).

The probability is

enter your response here.

(Round to four decimal places asneeded.)

Do the new ratings appear to be safe when the boat is loaded with16passengers? Choose the correct answer below.

A.

Because179.9 is greater than170, the new ratings do not appear to be safe when the boat is loaded with16 passengers.

B.

Because the probability of overloading is lower with the new ratings than with the oldratings, the new ratings appear to be safe.

C.

Because there is a high probability ofoverloading, the new ratings do not appear to be safe when the boat is loaded with

16 passengers.

D.

Because there is a high probability ofoverloading, the new ratings appear to be safe when the boat is loaded with16 passengers.