Use technology to solve the following problem: A ferry will safely accommodate 79 tons of passenger cars. Assume that the mean weight of a passenger car is 1.9 tons with standard deviation 0.5 tons. If a random sample of 39 cars are loaded onto the ferry, what is the probability that the Maximum safe weight will be exceeded?
A) 0.0516
B) 0.9417
C) 0.0583
D) 0.0669

Question

Quizplus · Accepted Answer

We can use the Central Limit Theorem to approximate the distribution of the sample mean weight of the 39 cars. The mean of the sample mean weight is still 1.9 tons, but the standard deviation of the sample mean weight is 0.5/sqrt(39) tons. To find the maximum safe weight, we need to find the weight of 79/39 = 2.0269 tons per car. We want to find the probability that the sample mean weight exceeds 2.0269 tons. 
Using the formula for a z-score, the z-score corresponding to 2.0269 tons is: z = (2.0269 - 1.9)/(0.5/sqrt(39)) = 1.488
Using a standard normal table or calculator, we find that the probability of a z-score exceeding 1.488 is 0.0669. Therefore, the probability that the maximum safe weight will be exceeded is 0.0669 or 6.69%, which is closest to choice C).

Use Technology to Solve the Following Problem: a Ferry Will