FE Civil · Chapter 2 · 4–6 exam questions

FE Civil Probability & Statistics

This chapter covers probability distributions, statistical inference, and regression — foundational tools for engineering data analysis.

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What the FE tests in Probability & Statistics

Descriptive Statistics

As a civil engineer, you compute means and standard deviations every time you evaluate concrete cylinder break tests, assess traffic count data, or summarize soil boring results. You fit regression curves to field data constantly — correlating SPT blow counts with soil shear strength, developing stage-discharge relationships, or establishing IDF curves for stormwater design. The spread in your data and the strength of your correlations tell you whether a design value is reliable.

Probability

As a civil engineer, probability distributions drive design — the 100-year flood follows a log-Pearson Type III distribution, traffic arrivals follow a Poisson distribution, and concrete strengths are modeled as normal. Expected values show up when comparing alternatives in benefit-cost analyses or compositing soil properties from multiple borings. You pick design values directly from these distributions.

Inferential Statistics

As a civil engineer, confidence intervals tell you how much to trust your field data — reporting a soil friction angle as 32° ± 3° at 95% confidence directly affects foundation design. Hypothesis testing tells you whether differences are real or noise: does a new concrete mix meet spec? Did a pavement treatment actually reduce accidents? These tools turn raw data into engineering decisions.

Key Probability & Statistics formulas

$\bar{x} = \frac{\sum x_i}{n}$
Sample MeanFE Handbook p. 63
$s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}$
Sample Std DevFE Handbook p. 63
$P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}$
Binomial DistributionFE Handbook p. 66
$z = \frac{x - \mu}{\sigma}$
Z-ScoreFE Handbook p. 67
$r = \frac{\sum(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum(x_i-\bar{x})^2\sum(y_i-\bar{y})^2}}$
Correlation CoefficientFE Handbook p. 69

Sample Probability & Statistics problems

Q1. A series of concrete cylinder tests yields compressive strengths (psi): 4200, 4350, 4100, 4500, 4250. What is the sample standard deviation?

Answer: 152 psi

Explain it simply

First find the mean: $(4200+4350+4100+4500+4250)/5 = 4280$ . Then compute each deviation squared, sum them, divide by $n-1$ (since it is sample, not population), and take the square root. The answer is about 152 psi. The trap is dividing by $n$ instead of $n-1$ .

Q2. A dataset has a mean of 50, a median of 45, and a mode of 42. What can be said about the distribution?

Answer: It is skewed right (positively skewed)

Explain it simply

When the mean is greater than the median and the median is greater than the mode, the distribution is skewed right (positively skewed). Think of it as a tail pulling the mean to the right. Left skew would have mean < median < mode.

These are 2 of 1,126 problems across all 15 chapters. The full bank, lessons, mastery tracking, and timed exam simulation live inside the app.

Common Probability & Statistics mistakes on the FE

Dividing by n instead of (n−1) for sample standard deviation — the FE uses the sample formula.
Confusing binomial and Poisson distributions — Poisson is for rare events over a continuous interval.
Forgetting to square the standard deviation to get variance, or vice versa.
Mixing up one-tailed and two-tailed hypothesis tests — read the problem statement carefully.

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