BSE Engineering Statistics and Data-Driven Decision Making 1 — Questions and Answers
Question 1: A manufacturing process produces components with a mean diameter of 50 mm and a standard deviation of 0.5 mm. What percentage of parts fall within ±2 standard deviations of the mean under a normal distribution?
- 68.27%
- 95.45% (Correct answer)
- 99.73%
- 90.00%
Correct answer: 95.45%
The empirical rule states that ±2 standard deviations from the mean captures approximately 95.45% of data in a normal distribution.
Question 2: In hypothesis testing, a Type II error occurs when:
- A true null hypothesis is rejected
- A false null hypothesis is not rejected (Correct answer)
- The significance level is set too low
- The sample size is too large
Correct answer: A false null hypothesis is not rejected
A Type II error (false negative) occurs when the null hypothesis is false but the test fails to reject it.
Question 3: Which control chart is most appropriate for monitoring the proportion of defective items in a production batch?
- X-bar chart
- R chart
- p-chart (Correct answer)
- c-chart
Correct answer: p-chart
The p-chart monitors the proportion (fraction) of defective items in samples, making it the correct choice for attribute data expressed as a proportion.
Question 4: An engineering manager wants to determine the relationship between machine age (years) and maintenance cost ($). Which statistical method is most appropriate?
- Chi-square test
- Simple linear regression (Correct answer)
- ANOVA
- Binomial distribution
Correct answer: Simple linear regression
Simple linear regression models the relationship between one independent variable (machine age) and one dependent variable (maintenance cost).
Question 5: The coefficient of variation (CV) is defined as:
- Mean divided by standard deviation
- Standard deviation divided by mean, expressed as a percentage (Correct answer)
- Variance divided by sample size
- Range divided by mean
Correct answer: Standard deviation divided by mean, expressed as a percentage
CV = (Standard Deviation / Mean) × 100%, and it measures relative variability, allowing comparison across datasets with different units or scales.
Question 6: In a factorial experiment with 3 factors each at 2 levels, how many treatment combinations are required for a full factorial design?
- 6
- 9
- 8 (Correct answer)
- 12
Correct answer: 8
A full 2³ factorial design requires 2³ = 8 treatment combinations, one for each unique combination of factor levels.
Question 7: Which probability distribution is most commonly used to model the time between failures of a system assuming a constant failure rate?
- Normal distribution
- Binomial distribution
- Exponential distribution (Correct answer)
- Poisson distribution
Correct answer: Exponential distribution
The exponential distribution models time between events in a Poisson process, making it ideal for systems with a constant (memoryless) failure rate.
BSE Engineering Statistics and Data-Driven Decision Making 1
A manufacturing process produces components with a mean diameter of 50 mm and a standard deviation of 0.5 mm.
What percentage of parts fall within ±2 standard deviations of the mean under a normal distribution?