The Fundamentals of Engineering Exam is the first licensing exam for engineers. You have to pass it on your way to becoming a professional engineer (PE). I was recently shown a problem from a review manual:

When it is operating properly, a chemical plant has a daily production rate that is normally distributed with a mean of 880 tons/day and a standard deviation of 21 tons/day. During an analysis period, the output is measured with random sampling on 50 consecutive days, and the mean output is found to be 871 tons/day. With a 95 percent confidence level, determine if the plant is operating properly.

- There is at least a 5 percent probability that the plant is operating properly.
- There is at least a 95 percent probability that the plant is operating properly.
- There is at least a 5 percent probability that the plant is not operating properly.
- There is at least a 95 percent probability that the plant is not operating properly.

Whoops…seems to be a problem there. I’m glad that engineers are expected to know some statistics; hopefully the engineering students taking the exam can spot the problem…but then how do they answer?