Statistics question

Question

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? Hint! Think about the average safe weight.

Answer 1

1.7(36) =61.2 tons for 36 cars and mean 1.7 tons, standard deviation = 1/2 ton

find z score for 66 tons

z = (66-61.2)/.5(36)

4.8/.5(36) = .2666... = z, .395 = 39.5% chance of exceeding 66 tons