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, and the arithmetic was re-run as an executable calculation. 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.
Standard Error of the Mean: FE Civil practice problem 1
For the Harbor District trunk sewer crossing, a survey coordinator preparing a post-event engineering review has a sample standard deviation of 180 psi from 32 concrete tests. What is the standard error of the sample mean?
- A22.05 psi
- B26.28 psi
- C31.82 psi
- D29.25 psi
Show the answer and worked solution
Answer: C — 31.82 psi
Worked solution
- Step 1. Use standard error of the mean
SE = s/sqrt(n)
- Step 2. Substitute values
SE = 180/sqrt(32) = 31.82 psi
Why the other choices are wrong
- Choice A
- Standard error of the mean equals the sample standard deviation divided by the square root of the sample size: 180 psi / sqrt(32) = 31.82 psi. This figure does not equal that quotient, and no single defensible slip in the formula, such as a wrong sample count, a missing square root, or a unit mix-up, reproduces it.
- Choice B
- Recomputing directly, 180 psi divided by the square root of 32 gives 31.82 psi as the true standard error of the mean. This number sits away from that result without tracing back to one clean arithmetic mistake, so the division should be redone rather than matched to a specific slip.
- Choice D
- The defensible calculation divides the given standard deviation by the square root of the 32-test sample, 180/5.657 = 31.82 psi. This listed figure diverges from that value, and it cannot be explained by a single formula substitution or sign error.