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A boat capsized and sank in a lake. Based on an assumption of a mean weight of 137 lb, the boat was rated to carry 50 passengers (so the load limit was 6,850 lb). After the boat sank, the assumed weight distribution is analyzed.

a) What is the probability that the actual weight of the boat exceeded 7,000 lb?

b) What is the probability that the actual weight of the boat was less than 6,500 lb?

c) What is the probability that the actual weight of the boat was between 6,700 lb and 6,900 lb?

d) What is the probability that the actual weight of the boat was exactly 6,800 lb?

Answer :

Without additional information about the distribution of passenger weights, we cannot calculate the exact probabilities of the boat's actual weight. Related problems involve calculating load capacity and addressing buoyancy safety concerns. Thus option d) What is the probability that the actual weight of the boat was exactly 6800 lb? is correct answer.

To answer questions about the probability of the actual weight of the boat, we would need to know the probability distribution of the weights of the passengers. Typically, such problems are solved using the normal distribution if the average and standard deviation are known. However, since no distribution or variance is provided in the question, it is not possible to calculate the exact probabilities requested without additional information.

For the related problems provided:

To find the mass of the load a barge can carry, we apply principles of buoyancy and calculate based on the submerged volume of the barge and the density of water.



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