Question

a boat capsized and sank in a lake. based on an assumption of a mean weight of 134 lb, the boat was rated to carry 70 passengers (so the load limit was 9,380 lb). after the boat sank, the assumed mean weight for similar boats was changed from 134 lb to 172 lb. complete parts a and b below.
a. assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 177.4 lb and a standard deviation of 40.1 lb. find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 134 lb.
the probability is 1.0000
(round to four decimal places as needed.)
b. the boat was later rated to carry only 15 passengers, and the load limit was changed to 2,580 lb. find the probability that the boat is overloaded because the mean weight of the passengers is greater than 172 (so that their total weight is greater than the maximum capacity of 2,580 lb).
the probability is 0.6985
(round to four decimal places as needed.)
do the new ratings appear to be safe when the boat is loaded with 15 passengers? choose the correct answer below.
a. because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with 15 passengers.
b. because 177.4 is greater than 172, the new ratings do not appear to be safe when the boat is loaded with 15 passengers.
c. because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 15 passengers.
d. because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe

Explanation:

Step1: Analyze part b result

The probability of over - loading when the boat is loaded with 15 passengers is 0.6985, which is relatively high.

Answer:

C. Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 15 passengers.