Mathematics, 12.02.2020 05:27, feefee945

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 lb, the boat was rated to carry 70 passengers (so the load limit was 9,660 lb). After the boat sank, the assumed mean weight for similar boats was changed from 138 lb to 173 lb. Complete parts a through c 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 179.4 lb. and a standard deviation of 37.7 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 138 lb.

The probability is .

(Round to four decimal places as needed)

b. The boat was later rated to carry only 17 passengers , and the load limit was changed to 2,941 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 173 ( so that their total weight is greater than the maximum capacity of 2,941 lb)

The probability is .

(Round to four decimal places as needed)

c. Do the new ratings appear to be safe when the boat is loaded with 17 passengers? Choose the correct answer below.

A. Because 179.4 is greater than 173, the new ratings do not appear to be safe when the boat is loaded with 17 passengers.

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

C. Because there is a high probability of overloading, the new ratings do not appear safe when the boat is loaded with 17 passengers.

D. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with 17 passengers.

Answers: 3

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A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 lb, the boat was...