Part 1. A boat capsized and sank in a lake. Based on an assumption of a mean weight of139lb, the boat was rated to carry60passengers (so the load limit was8,340 lb). After the boat sank, the assumed mean weight for similar boats was changed from139lb to174lb. Complete parts a and b below.

a.Assume that a similar boat is loaded with60passengers, and assume that the weights of people are normally distributed with a mean of180.1lb and a standard deviation of40.1lb. Find the probability that the boat is overloaded because the60passengers have a mean weight greater than139lb.

The probability is____.Round to four decimal places as needed.

b.The boat was later rated to carry only17passengers, and the load limit was changed to2,958lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than174(so that their total weight is greater than the maximum capacity of2, 958lb).

The probability is____. Round to four decimal places as needed.

Part. 2. Do the new ratings appear to be safe when the boat is loaded with17passengers? Choose the correct answer below.

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

B.Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with17passengers.

C.Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with17passengers.

D.Because180.1is greater than174,the new ratings do not appear to be safe when the boat is loaded with 17passengers.

Part 3.An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between140lb and201lb. The new population of pilots has normally distributed weights with a mean of 149 lband a standard deviation of27.6 lb.

a.If a pilot is randomly selected, find the probability that his weight is between140lb and201lb.

The probability is approximately____.(Round to four decimal places as needed.)

b.If40different pilots are randomly selected, find the probability that their mean weight is between140lb and201lb.The probability is approximately____.(Round to four decimal places as needed.)

c.When redesigning the ejection seat, which probability is more relevant?

A.Part (a) because the seat performance for a single pilot is more important.

B.Part (b) because the seat performance for a sample of pilots is more important.

C.Part (b) because the seat performance for a single pilot is more important.

D.Part (a) because the seat performance for a sample of pilots is more important.