Quality control, measurement error and reliability all rest on a handful of distributions and rules. Use the Handbook’s tables; don’t memorize them.
Choose any section below to get a free 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 median of 7, 3, 9, 1, 5, 8?
Sort: 1, 3, 5, 7, 8, 9. With six values, average the middle two: (5 + 7)/2 = 6.
Common trap: (B) forgets to sort first.
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. Try all of it free for 3 days →
Ask one question first: does order matter?
How many ways can a 1st, 2nd, 3rd and 4th place be awarded among 10 teams?
Order matters: P(10, 4) = 10 × 9 × 8 × 7 = 5040.
Common trap: (D) is C(10, 4), which ignores order.
permutationscombinationsThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
For independent events, multiply: P(A and B) = P(A)P(B).
A bin has 10 parts, 3 defective. Two are drawn without replacement. What is the probability both are defective?
(3/10)(2/9) = 6/90 = 0.0667.
Common trap: (A) is (3/10)2, which assumes replacement.
Probabilityconditional probabilityBayesThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
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).
For a binomial distribution with n = 20 and p = 0.3, what are the mean and variance?
μ = np = 6. σ2 = np(1 − p) = 20(0.3)(0.7) = 4.2.
Binomial DistributionPoisson DistributionThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Convert any normal variable to the standard (unit) normal with z = (x − μ)/σ, then read the probability from the Handbook’s table.
Scores are normal with μ = 100 and σ = 15. What fraction fall between 85 and 115?
That is z = −1 to +1: 0.683.
Common trap: (C) is only one side, 0 to 1.
Normal DistributionUnit Normal DistributionThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
A least-squares line ŷ = a + bx has slope b = Sxy/Sxx and passes through the point (x̄, ȳ).
A least-squares fit gives ŷ = 2.2 + 0.6x. What is the predicted y at x = 6?
ŷ = 2.2 + 0.6(6) = 5.8.
Least SquaresConfidence Intervalcorrelation coefficientThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
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