The standard error of the mean measures how much a sample average would bounce around if you repeated the sampling, and it is the bridge between a set of measurements and a confidence interval. It is the sample standard deviation divided by the square root of the sample size, and the square root is the entire point. Quadrupling the sample size halves the standard error, which is why precision improves slowly and expensively as a survey or a materials testing program grows. On the FE Civil exam the question usually arrives in one of two forms: compute the standard error from a standard deviation and a sample size, or build a confidence interval around a sample mean. The confidence interval is the mean plus and minus a critical value times the standard error, and the critical value comes from the normal distribution when the population standard deviation is known or the sample is large. Keep the two spread measures separate in your head. The standard deviation describes how much individual observations scatter and does not shrink as you collect more data. The standard error describes how much the average of those observations scatters and does shrink. Substituting one for the other, or dividing by n rather than by the square root of n, produces the two most common wrong answers.
Commit to an answer before opening the solution. Each problem shows the governing model, every substitution, a unit check, and why each wrong choice is wrong.
Original question written by FE Exam AI Prep from the public FE Civil exam specification. Before release, a solver model re-derived the answer twice from the question alone, without its answer key, and a critic model checked the result. No licensed engineer reviews these questions. It is not an NCEES question and does not come from any NCEES practice exam. FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES.
FE Exam AI Prep is an independent study tool and is not affiliated with, endorsed by, or sponsored by NCEES. All practice questions are original and generated for study purposes based on publicly available exam specifications.