FE Other Disciplines Probability and Statistics

Knowledge area 2 of the FE Other Disciplines exam: 6–9 of the 110 questions. The subtopics NCEES lists, how they are tested and worked practice problems with solutions.

Take a full timed FE Other Disciplines practice exam

110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.

Or start the free Probability and Statistics drill

What the specification lists

Estimation (e.g., point, confidence intervals)
Expected value and expected error in decision making
Sample distributions and sizes (e.g., significance, hypothesis testing, non-normal distributions)
Goodness of fit (e.g., correlation coefficient, standard errors, R²)

From the NCEES FE Other Disciplines CBT exam specifications, knowledge area 2.

Line drawing of a bell curve on a whiteboard, a pair of dice and a scatter of points with a trend line

How Probability and Statistics is tested

Expect a mean, a standard deviation, a normal-distribution probability with a z value, a confidence interval or a regression line. Practice reading the unit normal table in the Reference Handbook section on engineering probability and statistics, and know when to use the sample (n − 1) rather than the population standard deviation.

On exam day the relationships you need are in the Reference Handbook section on Engineering Probability and Statistics. The handbook is the only reference allowed, so practice finding each formula in it rather than memorizing a separate sheet.

Start the free Probability and Statistics drill

FE Other Disciplines Probability and Statistics practice problems

Work each problem with your calculator and the handbook, then open the solution.

Problem 1 · Probability distributions

Machined rod lengths are normally distributed with a mean of 250.0 mm and a standard deviation of 0.8 mm. The specification limits are 248.8 mm and 251.6 mm. For the standard normal distribution, Φ(1.50) = 0.9332 and Φ(2.00) = 0.9772. Enter the percentage of rods that fall within the specification, to one decimal place.

Fill in the blank: answer in %.

Show the answer and solution

Answer: 91 % (accepted 90.5 to 91.5)

z₁ = (248.8 − 250.0)/0.8 = −1.50 and z₂ = (251.6 − 250.0)/0.8 = 2.00. P = Φ(2.00) − Φ(−1.50) = 0.9772 − (1 − 0.9332) = 0.9104, or 91.0%. The limits are not symmetric about the mean, so a single ±z value does not apply.

Probability distributions · Reference Handbook: Engineering Probability and Statistics

Problem 2 · Estimation

A sample x₁, x₂, ..., xₙ with mean x̄ is drawn from a population. The unbiased point estimator of the population variance σ² is:

A.Σ(xᵢ − x̄)²/(n − 1)
B.Σ(xᵢ − x̄)/(n − 1)
C.Σ(xᵢ − x̄)²/n
D.√[Σ(xᵢ − x̄)²/(n − 1)]

Show the answer and solution

Answer: A: Σ(xᵢ − x̄)²/(n − 1)

Because x̄ is computed from the same data, the squared deviations about x̄ are on average smaller than those about μ. Dividing by n − 1 instead of n corrects that bias, so s² = Σ(xᵢ − x̄)²/(n − 1) has expected value σ².

Estimation · Reference Handbook: Engineering Probability and Statistics

Problem 3 · Goodness of fit

A linear regression of pavement roughness against age has a negative slope. The error sum of squares is SSE = 14.2 and the total sum of squares is SST = 182.6. The correlation coefficient r is most nearly:

A.−0.960
B.−0.922
C.0.922
D.0.960

Show the answer and solution

Answer: A: −0.960

R² = 1 − SSE/SST = 1 − 14.2/182.6 = 0.922. |r| = √0.922 = 0.960, and r takes the sign of the slope, so r = −0.960.

Goodness of fit · Reference Handbook: Engineering Probability and Statistics

Problem 4 · Measures of central tendencies and dispersions

Five mortar cubes tested at 7 days gave compressive strengths of 28.4, 31.0, 30.2, 33.5, and 29.9 MPa. Using the sample standard deviation, enter the coefficient of variation in percent, to one decimal place.

Fill in the blank: answer in %.

Show the answer and solution

Answer: 6.1 % (accepted 6 to 6.2)

Mean = 153.0/5 = 30.60 MPa. Sample standard deviation s = 1.875 MPa (dividing the sum of squared deviations, 14.06 MPa², by n − 1 = 4). CV = s/x̄ × 100 = 1.875/30.60 × 100 = 6.1%. Dividing by n instead gives 5.5%.

Measures of central tendencies and dispersions · Reference Handbook: Engineering Probability and Statistics

More FE Other Disciplines practice problems from every knowledge area

Sit the full exam under the real clock

Take a full timed FE Other Disciplines practice exam

110 questions on the real 5 hours 20 minutes clock, weighted to the NCEES specifications, with a score by knowledge area and a worked solution for every answer.

Or start the free Probability and Statistics drill

Common questions

How many Probability and Statistics questions are on the FE Other Disciplines exam?

The NCEES FE Other Disciplines specification lists 6–9 questions on Probability and Statistics, out of 110. Every examinee gets the same number per knowledge area.

What does Probability and Statistics cover on the FE Other Disciplines exam?

Estimation (e.g., point, confidence intervals); Expected value and expected error in decision making; Sample distributions and sizes (e.g., significance, hypothesis testing, non-normal distributions); Goodness of fit (e.g., correlation coefficient, standard errors, R²).

Where are the Probability and Statistics formulas on exam day?

In the NCEES FE Reference Handbook, which appears on screen during the exam: the Engineering Probability and Statistics section. Practice with your free copy from MyNCEES so you know where each relationship sits.

Original independent practice questions written to the published NCEES exam specifications. Not affiliated with or endorsed by NCEES (National Council of Examiners for Engineering and Surveying).