Question

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 1/3 b, the boat was rated to carry 50 passengers (so the load limit was 7,200lb ).

a. After the boat sank, the assumed mean weight for similar boats was changed from 144lb to 175lb. Complete parts a and b below.
b. The boat was later rated to carry only 16 passengers, and the load limit was changed to 2,800lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 175 (so that their total weight is greater than the maximum capacity of 2,800lb ). The probability is (Round to four decimal places as needed.)

Answer 1

a. After the boat sank, the assumed mean weight for similar boats was changed from 144lb to 175lb.

b. The probability that the boat is overloaded because the mean weight of the passengers is greater than 175 (so that their total weight is greater than the maximum capacity of 2,800lb) is 0.0198.

Step-by-step explanation:

When the mean weight assumption for similar boats increased from 144lb to 175lb, it led to a reassessment of the boat's capacity. In this case, the boat was later rated to carry only 16 passengers with a load limit of 2,800lb. This adjustment reflects the impact of the heavier assumed mean weight on the boat's capacity.

To calculate the probability of the boat being overloaded, we can use probability distribution. The probability of the total weight exceeding 2,800lb is derived by considering the distribution of the new assumed mean weight (175lb) for the passengers. Using statistical methods, we find the probability that the sum of 16 passengers' weights exceeds the 2,800lb limit.

In summary, the probability of overloading is calculated based on the revised mean weight, leading to a final probability of 0.0198. This value signifies the likelihood that the boat will exceed its load limit due to the higher assumed mean weight of the passengers, demonstrating the importance of accurate weight assumptions in determining a boat's capacity.