BSIE Probability & Statistics 2 — Questions and Answers
Question 1: A process has a defect rate of 2%. In a sample of 200 items, what is the expected number of defects?
- 2
- 4 (Correct answer)
- 6
- 8
Correct answer: 4
Expected value = n × p = 200 × 0.02 = 4 defects.
Question 2: Which measure of central tendency is most resistant to outliers?
- Mean
- Median (Correct answer)
- Mode
- Weighted average
Correct answer: Median
The median is resistant to outliers because it depends only on the middle value(s), not the magnitude of extreme values.
Question 3: In a normal distribution, approximately what percentage of data falls within ±2 standard deviations of the mean?
- 68%
- 90%
- 95% (Correct answer)
- 99.7%
Correct answer: 95%
The empirical rule states that approximately 95% of data falls within ±2 standard deviations of the mean.
Question 4: Two events A and B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is P(A ∪ B)?
- 0.12
- 0.58
- 0.70 (Correct answer)
- 1.00
Correct answer: 0.70
For mutually exclusive events, P(A ∪ B) = P(A) + P(B) = 0.3 + 0.4 = 0.7.
Question 5: A production line fills bottles with a mean of 500 mL and standard deviation of 5 mL. What is the z-score for a bottle containing 512 mL?
- 1.2
- 2.0
- 2.4 (Correct answer)
- 2.8
Correct answer: 2.4
z = (x − μ) / σ = (512 − 500) / 5 = 12 / 5 = 2.4.
Question 6: Which distribution is most appropriate to model the number of customer arrivals at a service desk per hour?
- Normal
- Binomial
- Poisson (Correct answer)
- Exponential
Correct answer: Poisson
The Poisson distribution models the count of independent events occurring in a fixed interval of time.
Question 7: The coefficient of variation (CV) is defined as:
- Mean divided by variance
- Standard deviation divided by mean, expressed as a percentage (Correct answer)
- Variance divided by mean
- Range divided by standard deviation
Correct answer: Standard deviation divided by mean, expressed as a percentage
CV = (σ / μ) × 100%, providing a relative measure of dispersion independent of units.
BSIE Probability & Statistics 2
A process has a defect rate of 2%.
In a sample of 200 items, what is the expected number of defects?