A ferry will safely accommodate 66 tons of passenger cars. Assume that the mean weight of a passenger car is 1.7 tons with standard deviation 0.5 tons. If a random sample of 36 cars are loaded onto the ferry, what is the probability that the maximum safe weight will be exceeded?

Question

Quizplus · Accepted Answer

The probability that the maximum safe weight will be exceeded is the probability that the sample mean weight of the 36 cars is greater than 66/36 = 1.83 tons. The sample mean weight is normally distributed with mean 1.7 tons and standard deviation 0.5/sqrt(36) = 0.0833 tons. The probability that the sample mean weight is greater than 1.83 tons is the area under the normal curve to the right of 1.83 tons, which is 0.0548.

A Ferry Will Safely Accommodate 66 Tons of Passenger Cars