Question

# A boat capsized and sank in a lake. Based on an assumption of mean weight of...

A boat capsized and sank in a lake. Based on an assumption of mean weight of 146146 ​lb, the boat was rated to carry 5050 passengers​ (so the load limit was 7 comma 3007,300 ​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from146146 lb to170170 lb. Complete parts a and b below.

a. Assume that a similar boat is loaded with 5050 ​passengers, and assume that the weights of people are normally distributed with a mean of 177.3177.3 lb and a standard deviation of 39.439.4 lb. Find the probability that the boat is overloaded because the 5050 passengers have a mean weight greater than 146146 lb.

The probability is?

b. The boat was later rated to carry only 1515 ​passengers, and the load limit was changed to 2 comma 5502,550 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 170170 ​(so that their total weight is greater than the maximum capacity of 2 comma 5502,550 ​lb).

The probability is?

Do the new ratings appear to be safe when the boat is loaded with 1515 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 1515 passengers.

B.Because 177.3177.3 is greater than 170170​, the new ratings do not appear to be safe when the boat is loaded with 1515 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 1515 passengers.

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