a boat capsized and sank in a lake. based on an assumption of a mean weight of 139 lb, the boat was rated to carry 50 passengers (so the load limit was 6 comma 950 lb). after the boat sank, the assumed mean weight for similar boats was changed from 139 lb to 173 lb. complete parts a and b below.
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 176.8 lb and a standard deviation of 39.5 lb. find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 139 lb.
the probability is
nothing.
(round to four decimal places as needed.)
b. the boat was later rated to carry only 14 passengers, and the load limit was changed to 2 comma 422 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 comma 422 lb).
the probability is
nothing.
(round to four decimal places as needed.)
do the new ratings appear to be safe when the boat is loaded with 14 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 14 passengers.
b.
because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 14 passengers.
c.
because 176.8 is greater than 173, the new ratings do not appear to be safe when the boat is loaded with 14 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.