Descriptive statistics, counting, probability, the binomial and normal distributions, regression and confidence intervals: the statistics half of the FE Civil’s Mathematics and Statistics area.
NCEES lists these Mathematics and Statistics topics for the FE Civil: analytic geometry; single-variable calculus; vector operations; statistics: distributions, mean, mode, standard deviation, confidence intervals, regression and curve fitting; probability: estimation and expected value. On Newton’s Notes this area spans 4 chapters: this one and Analytic Geometry and Trigonometry, Algebra and Linear Algebra and Calculus.
Choose any section below to get a free FE Civil practice problem. Work it with the FE Reference Handbook open, tap your answer, then check the solution.
The mean is the balance point and the median is the middle value.
What is the population standard deviation of 2, 4, 4, 4, 5, 5, 7, 9?
Mean 5. Squared deviations sum to 32. σ2 = 32/8 = 4, σ = 2.00.
Common trap: (D) divides by n − 1 (sample). (A) is the variance.
Dispersion, Mean, Median, and Modestandard deviationThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Ask one question first: does order matter?
A team needs 2 engineers from 6 candidates and 1 technician from 4. How many teams are possible?
C(6, 2) × C(4, 1) = 15 × 4 = 60.
Common trap: (B) uses P(6, 2) = 30, counting each pair twice.
permutationscombinationsThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
For independent events, multiply: P(A and B) = P(A)P(B).
2% of parts are defective. A test flags 95% of defective parts and 5% of good parts. If a part is flagged, what is the probability it is defective?
P(flag) = 0.02(0.95) + 0.98(0.05) = 0.019 + 0.049 = 0.068. P(defective | flag) = 0.019/0.068 = 0.279.
Common trap: (B) confuses P(flag | defective) with P(defective | flag).
Probabilityconditional probabilityBayesThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
The binomial distribution counts successes in n independent trials with the same probability p: P(x) = C(n, x)px(1 − p)n−x, with mean np and variance np(1 − p).
Calls arrive at an average of 2 per hour (Poisson). What is the probability of no calls in an hour?
P(0) = e−2 = 0.135.
Common trap: (A) is P(1) = 2e−2.
Binomial DistributionPoisson DistributionThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Convert any normal variable to the standard (unit) normal with z = (x − μ)/σ, then read the probability from the Handbook’s table.
Bolt lengths are normal with μ = 50.0 mm and σ = 0.2 mm. What fraction is longer than 50.5 mm?
z = 0.5/0.2 = 2.5. P(z > 2.5) = 1 − 0.9938 = 0.0062.
Common trap: (B) is P(z < 2.5); the question asks for the tail.
Normal DistributionUnit Normal DistributionThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
A least-squares line ŷ = a + bx has slope b = Sxy/Sxx and passes through the point (x̄, ȳ).
A sample of n = 16 has x̄ = 50 and known σ = 4. What is the 95% confidence interval for the mean?
σ/√n = 4/4 = 1. 50 ± 1.96(1) = 48.04 to 51.96.
Common trap: (C) forgets to divide σ by √n.
Least SquaresConfidence Intervalcorrelation coefficientThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Start your 3-day free trial →
Newton’s Notes FE Civil has 18 chapters (11 shared with Mechanical, 7 Civil-only) with lessons, worked examples and 420+ FE-style practice problems with full solutions, 171 of them Civil-only. Pro adds a timed full-length FE Civil practice exam (110 problems), a custom test builder and Ask Newton, the AI tutor. Try it free for 3 days, no card to start.
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