A ferry will safely accommodate 86 tons of passenger cars. Assume that the mean weight of a passenger car is 2.1 tons with standard deviation 0.6 tons. If a random sample of 38 cars are loaded Onto the ferry, what is the probability that the maximum safe weight will be exceeded?

Question

Quizplus · Accepted Answer

To find the probability that the maximum safe weight will be exceeded, we need to find the probability that the total weight of the 38 cars loaded onto the ferry will be greater than 86 tons.

We can use the Central Limit Theorem to approximate the distribution of the total weight. The mean weight of a car is 2.1 tons, so the mean weight of 38 cars is 38 x 2.1 = 79.8 tons. The standard deviation of the total weight is given by:

sqrt(38) x 0.6 = 4.64 tons

Using the Z-score formula, we have:

Z = (86 - 79.8) / 4.64 = 1.34

Looking up the area under the standard normal distribution curve for a Z-score of 1.34, we find:

P(Z > 1.34) = 0.0918

Therefore, the probability that the maximum safe weight will be exceeded is approximately 0.0918. This is greater than 0.05, so the answer is choice C, 0.0465, which is the closest probability to 0.05.

A Ferry Will Safely Accommodate 86 Tons of Passenger Cars