Lean Six Sigma Green Belt Certification Lean Six Sigma Green Belt Basic Statistical Tools 1 — Questions and Answers
Question 1: In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?
- 68.3%
- 95.4% (Correct answer)
- 99.7%
- 90.0%
Correct answer: 95.4%
The empirical rule states that ~68% of data falls within ±1σ, ~95.4% within ±2σ, and ~99.7% within ±3σ of the mean in a normal distribution.
Question 2: A scatter diagram is primarily used to:
- Display the frequency distribution of a single variable
- Identify the relationship between two continuous variables (Correct answer)
- Track a process metric over time
- Rank defect categories by frequency
Correct answer: Identify the relationship between two continuous variables
A scatter diagram plots paired data points to visually reveal whether a relationship (positive, negative, or none) exists between two continuous variables.
Question 3: Which of the following best describes a process capability index (Cp) value of 1.33?
- The process is barely meeting specification limits
- The process is centered and highly capable (Correct answer)
- The process mean is shifted from the target
- The process is not capable of meeting specifications
Correct answer: The process is centered and highly capable
A Cp of 1.33 means the process spread fits within the specification limits with adequate margin (process width is 75% of the spec width), indicating a capable process. Cp does not account for centering—that is Cpk.
Question 4: What does a p-value less than 0.05 indicate in hypothesis testing (assuming α = 0.05)?
- There is a 5% chance the null hypothesis is true
- We fail to reject the null hypothesis
- The result is statistically significant and we reject the null hypothesis (Correct answer)
- The sample size is too small to draw conclusions
Correct answer: The result is statistically significant and we reject the null hypothesis
When the p-value is less than the significance level α (0.05), the evidence against the null hypothesis is strong enough to reject it, meaning the result is statistically significant.
Question 5: In a box plot (box-and-whisker plot), what does the line inside the box represent?
- The mean of the data set
- The median (50th percentile) (Correct answer)
- The mode of the data set
- One standard deviation from the mean
Correct answer: The median (50th percentile)
The line inside the box of a box plot marks the median (Q2 or 50th percentile). The box itself spans from Q1 (25th percentile) to Q3 (75th percentile), representing the interquartile range.
Question 6: Which type of control chart is most appropriate for monitoring the proportion of defective items in a sample?
- X-bar and R chart
- I-MR chart
- p-chart (Correct answer)
- c-chart
Correct answer: p-chart
A p-chart tracks the proportion (fraction) of nonconforming items per sample and is used for attribute data where each unit is classified as defective or not. The c-chart tracks the count of defects per unit, X-bar/R tracks continuous measurements, and I-MR is for individual continuous measurements.
Lean Six Sigma Green Belt Certification Lean Six Sigma Green Belt Basic Statistical Tools 1
In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?