Question

A boat capsized and sank in a lake. Based on an assumption of a mean weight of146​lb, the boat was rated to carry 50 passengers​ (so the load limit was 7,300​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 146lb to170lb. Complete parts a and b below.

A) a. Assume that a similar boat is loaded with 50 ​passengers, and assume that the weights of people are normally distributed with a mean of 177.3lb and a standard deviation of 39.4lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 146lb. The probability is

B) b. The boat was later rated to carry only 15 ​passengers, and the load limit was changed to 2,550 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 170​(so that their total weight is greater than the maximum capacity of 2,550 ​lb). The probability is

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 do not appear to be safe when the boat is loaded with 15 passengers.

B.Because 177.3 is greater than170 the new ratings do not appear to be safe when the boat is loaded with 15 passengers.

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

D.Because there is a high probability of​ overloading, the new ratings appear to be safe when the boat is loaded with 15 passengers.

Answer 1