All Free Quantitative Methods MCQs with Answers

• A. 1/6
• B. 5/18
• C. 25/36
• D. 11/36

Explanation: The probability of no six in two rolls is (5/6)^2 = 25/36. Therefore, the probability of at least one six is 1 - 25/36 = 11/36.

• A. 0.3
• B. 0.7
• C. 0.9
• D. 1.1

Explanation: The addition rule gives P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Thus, the result is 0.5 + 0.4 - 0.2 = 0.7.

• A. 0.49
• B. 0.70
• C. 1.10
• D. 1.70

Explanation: The mean is E(X) = 1.1 and E(X²) = 1.7. Hence, Var(X) = E(X²) - [E(X)]² = 1.7 - 1.21 = 0.49.

• A. 0.1024
• B. 0.1536
• C. 0.2304
• D. 0.3456

Explanation: Use the binomial formula: C(5,3)(0.4)^3(0.6)^2. This equals 10 × 0.064 × 0.36 = 0.2304.

• A. e^-1
• B. 1 - e^-3
• C. 3e^-3
• D. e^-3

Explanation: For a Poisson variable, P(X = x) = e^-λ λ^x/x!. When x = 0 and λ = 3, this becomes e^-3.

• A. 0.25
• B. 2
• C. 4
• D. 5

Explanation: The number of attempts until the first success follows a geometric distribution. Its expected value is 1/p, so 1/0.25 = 4 attempts.

• A. 1/6
• B. 1/3
• C. 1/2
• D. 2/3

Explanation: For a uniform distribution, probability equals the length of the required interval divided by the total length.

• A. 1
• B. 2
• C. 7
• D. 20

Explanation: The standardized value is z = (X - μ)/σ. Substituting the values gives z = (70 - 50)/10 = 2.

• A. Equal to its variance
• B. Always 1
• C. Equal to its mean
• D. Always 0

Explanation: For a continuous random variable, probability is assigned to intervals, not individual points.

• A. 0.8
• B. 4
• C. 5
• D. 20

Explanation: The standard error of the sample mean is σ divided by the square root of n. Thus, it is 20/√25 = 20/5 = 4.

• A. 1/169
• B. 1/221
• C. 1/256
• D. 1/265

Explanation: There are 4 aces among 52 cards, so the probability of an ace first and another ace second is (4/52)(3/51) = 1/221.

• A. 1.6
• B. 2.0
• C. 2.4
• D. 4.0

Explanation: For a binomial variable, variance equals np(1 − p). Thus, Var(X) = 10(0.4)(0.6) = 2.4, not np, which is the expected value.

• A. 2e⁻²
• B. 1 − 2e⁻²
• C. e⁻²/2
• D. 4e⁻²

Explanation: The Poisson probability formula is P(X = x) = e⁻λ λˣ/x!. Substituting λ = 2 and x = 2 gives e⁻²(2²/2!) = 2e⁻².

• A. 273/760
• B. 189/760
• C. 91/380
• D. 7/20

Explanation: This is a hypergeometric probability because selection occurs without replacement.

• A. 0.3413
• B. 0.5000
• C. 0.6826
• D. 0.9544

Explanation: The central interval from one standard deviation below the mean to one above the mean contains about 68.26 percent of a normal…

• A. 4
• B. 6
• C. 7
• D. 10

Explanation: The mean of a uniform distribution on [a, b] is (a + b)/2. Therefore, the expected value is (4 + 10)/2 = 7.

• A. The number of trials is random
• B. Each trial has more than two outcomes
• C. The success probability changes each trial
• D. The trials are independent with fixed success probability

Explanation: A binomial model requires a fixed number of independent trials, two outcomes per trial, and a constant success probability.

• A. 1/6
• B. 1/2
• C. 2/3
• D. 5/6

Explanation: The density is constant, so the probability equals the interval length multiplied by the density. Hence P(2 ≤ X ≤ 5) = (5 − 2)(1/6) = 1/2.

• A. 9
• B. 16
• C. 36
• D. 81

Explanation: For a linear transformation, Var(aX + b) = a²Var(X), while the constant b has no effect.

• A. Mean 36, variance 75
• B. Mean 38, variance 75
• C. Mean 36, variance 225
• D. Mean 38, variance 225

Explanation: The mean transforms as E(Y) = 3E(X) + 2 = 38. The variance is multiplied by the square of the coefficient, so Var(Y) = 3² × 25 = 225.