ISYE 6501 –ACTUAL EXAM 70 QUESTIONS ANSWERS & RATIONALES.
SECTION 1 — PROBABILITY & STATISTICS
1. The probability that event A occurs is 0.3 and B is 0.4. If A and B are
independent, P(A ∩ B) = ?
A. 0.12
B. 0.70
C. 0.10
D. 0.03
Answer: A
Rationale: Independence → multiply: 0.3 × 0.4 = 0.12.
2. Variance of a constant c is:
A. c
B. c²
C. 0
D. Undefined
Answer: C
Rationale: A constant does not vary → variance = 0.
3. The expected value of a discrete variable 𝑿is computed as:
A. Sum of probabilities
B. Sum of values
,C. ∑ x·P(x)
D. ∑ x/P(x)
Answer: C
Rationale: Basic expectation formula.
4. A fair die is rolled twice. P(sum = 7)?
A. 1/6
B. 1/12
C. 1/36
D. 1/8
Answer: A
Rationale: 6 combinations sum to 7 out of 36 → 6/36 = 1/6.
5. Central Limit Theorem states:
A. Small samples are always normal
B. Sample mean is normally distributed as n → ∞
C. Population becomes normal
D. Variance decreases to zero
Answer: B
Rationale: CLT applies to the sampling distribution of the mean.
6. Standard error of the mean = ?
A. σ
B. σ²
C. σ / √n
D. √σ / n
, Answer: C
7. A 95% CI means:
A. 95% of population is inside interval
B. 95% chance sample mean is inside
C. 95% of repeated intervals contain true μ
D. 95% of data is within 2σ
Answer: C
8. A Type I error occurs when:
A. You reject a true H₀
B. You accept a true H₀
C. You fail to reject false H₀
D. You reject false H₀
Answer: A
9. Increasing sample size…
A. Increases CI width
B. Decreases standard error
C. Increases p-values
D. Has no effect on power
Answer: B
10. A p-value of 0.03 means:
SECTION 1 — PROBABILITY & STATISTICS
1. The probability that event A occurs is 0.3 and B is 0.4. If A and B are
independent, P(A ∩ B) = ?
A. 0.12
B. 0.70
C. 0.10
D. 0.03
Answer: A
Rationale: Independence → multiply: 0.3 × 0.4 = 0.12.
2. Variance of a constant c is:
A. c
B. c²
C. 0
D. Undefined
Answer: C
Rationale: A constant does not vary → variance = 0.
3. The expected value of a discrete variable 𝑿is computed as:
A. Sum of probabilities
B. Sum of values
,C. ∑ x·P(x)
D. ∑ x/P(x)
Answer: C
Rationale: Basic expectation formula.
4. A fair die is rolled twice. P(sum = 7)?
A. 1/6
B. 1/12
C. 1/36
D. 1/8
Answer: A
Rationale: 6 combinations sum to 7 out of 36 → 6/36 = 1/6.
5. Central Limit Theorem states:
A. Small samples are always normal
B. Sample mean is normally distributed as n → ∞
C. Population becomes normal
D. Variance decreases to zero
Answer: B
Rationale: CLT applies to the sampling distribution of the mean.
6. Standard error of the mean = ?
A. σ
B. σ²
C. σ / √n
D. √σ / n
, Answer: C
7. A 95% CI means:
A. 95% of population is inside interval
B. 95% chance sample mean is inside
C. 95% of repeated intervals contain true μ
D. 95% of data is within 2σ
Answer: C
8. A Type I error occurs when:
A. You reject a true H₀
B. You accept a true H₀
C. You fail to reject false H₀
D. You reject false H₀
Answer: A
9. Increasing sample size…
A. Increases CI width
B. Decreases standard error
C. Increases p-values
D. Has no effect on power
Answer: B
10. A p-value of 0.03 means:
