Practice Exam
Page 1
Practice Black Belt Certification Exam
(50 Questions + 10 Optional Questions & Certified
Answers) The Ultimate Guide for 2026/2027
This is a practice test. Although many of the ‘topics’ in the questions below will be on the final
certification exam, other topics will be tested. Students should also review their exercise
questions and case studies for additional key course concepts.
Section 1. General
1) Which of the following Six Sigma tools/methods is typically used to define a problem or
improvement opportunity (including what, when, extent) and the potential impact in terms of
business performance for resolving the problem (e.g., operating costs)?
a. Project planning matrix
b. Project charter
c. Value stream map
d. Performance diagram (P-Diagram)
See NOTES. Project Charter includes the What, When, Extent, and Impact of the problem. Project
Planning/Prioritization Matrix helps determine which projects in the pipeline to select to and
work on. Value Stream Map documents the actions to get a product/service to the customer.
PDiagram analyzes potential causes by documenting key process inputs and outputs.
2) Given the following statistical results, which of the following may be reasonably concluded?
a. No evidence to suggest data are not Normally Distributed
b. Data are skewed right
, Practice Exam
Page 2
c. Data are skewed left
d. Sample size is too low to conduct a Normality Test
See NOTES. Skewness value of 1.597 suggests that the distribution is not normally distributed (eliminate
answer A). A positive skew value suggested skewed right (answer B and eliminate answer C). Sample size
(N) = 50 and is large enough to conduct a normality test (eliminate answer D).
3) Which of the following statistics are displayed for the ‘box’ portion of a box plot?
a. Mean + 3 standard deviations
b. Median + 2 standard deviations
c. 1st Quartile, Median, and 3rd Quartile
d. Mean + 2 standard deviations
See NOTES. The box shows the 25th to 75th percentile (Quartile 1 to Quartile 3). The bottom line is the 1st
quartile, the middle line is the median, and the top line is the 3rd quartile.
4) What is the rolled yield of a 5-step serial process with the following yields for each step?
Step 1: 0.85; Step 2: 0.94; Step 3: 0.64; Step 4: 0.98; Step 5: 0.95
Assume each step is based on defective/not defective (Binary – Binomial).
a. 47.61%
b. 86.2%
c. 87.2%
d. 100%
Rolled Yield = 0.85*0.94*0.64*0.98*0.95 = 0.4761 = 47.61%
5) Suppose you inspect car doors on finished vehicles. For each door, you check for paint quality defects,
out-of-alignment areas of the door, and out-of-flush areas of the door between the front fender. If you
wish to visually show where on the door most of the defects are appearing, which of the following tools
would you most likely use?
a. Cause-Effect Diagram (Fishbone Diagram)
b. P-Diagram
c. Defect Location Check Sheet
d. Either (a) or (b)
, Practice Exam
Page 3
See NOTES. Defect Location Check Sheet shows visual location of issues. Cause-Effect Diagrams and
PDiagrams analyze potential causes.
6) A billing representative examines reasons for denial of payment after claims submission. A
check sheet is used to record the frequency of some common submittal problems. The data are
summarized in the following table.
Claim Defect Reason Frequency
Missing insurance number 15
Days of care wrong 10
Services provided incorrect 21
Referral information missing 2
Typo 4
Other 5
Total 57
Given the above table for denial of claims, what would be the cumulative relative frequency
for the category “missing insurance number” after performing a Pareto Analysis?
a. 63%
b. 44%
c. 26%
d. 80%
, Practice Exam
Page 4
7) Suppose you work for an office furniture manufacturer and you inspect outgoing products
(desks, credenza, etc.). Any given product may have multiple defects (1 or more per unit). Given
the following inspection data, which of the following would be most representative of the
current state of this process? (Assume that drawers cannot simultaneously have a gap that is ‘too
wide’ and ‘too narrow’ for a given manufactured unit and that Yield may be estimated using
DPU based on a Poisson distribution).
Gap Gap
Between Between
Excess Excess Drawers Drawers Missing
# Units Scratches Chips too wide too narrow Piece
Desk (w/two drawers) 200 5 4 3 6 2
Credenza (w/ 2 drawers) 190 7 2 1 0 3
File Cabinet (w/ 2 drawers) 210 9 1 2 6 2
Book Case 75 4 3 N/A N/A N/A
Total 675 25 10 6 12 7
N/A - not applicable
a. DPMO=3.4 (Yield = 99.99966%)
b. DPMO=17,778 (Yield = 1.8%)
c. DPMO=19,048 (Yield = 98%)
d. DPMO=23,529 (Yield = 91.5%)
The two ‘gap between drawer’ categories should be treated as a single opportunity because they
cannot both happen simultaneously. So, the first three furniture types have 4 defect
opportunities per unit: excess scratches, excess chips, gap between drawers, and missing piece.
Book cases only have 2 opportunities per unit: excess scratches, and excess chips.
Total Defects = 25 + 10 + 6 + 12 + 7 = 60
Total Opportunities = (200 * 4 per unit)+(190 * 4 per unit)+(210 * 4 per unit)+(75 * 2 per unit) =
2550
DPMO = Total # Defects / Total Opportunities x 1 million = * 1,000,000 = 23,529.4
Defect per Unit (DPU) = Total # Defects / Total # Units = = 0.08889
Yield (assuming Poisson) = Pr(K=0) = e-dpu = e-0.08889 = 0.91495 = 91.5%
8) For the above furniture problem, suppose you estimate the average cost to repair each of the
defect types (see last row in table below). Based on a Pareto Analysis and the primary objective
of a DMAIC project, which defect type should be addressed first?
Page 1
Practice Black Belt Certification Exam
(50 Questions + 10 Optional Questions & Certified
Answers) The Ultimate Guide for 2026/2027
This is a practice test. Although many of the ‘topics’ in the questions below will be on the final
certification exam, other topics will be tested. Students should also review their exercise
questions and case studies for additional key course concepts.
Section 1. General
1) Which of the following Six Sigma tools/methods is typically used to define a problem or
improvement opportunity (including what, when, extent) and the potential impact in terms of
business performance for resolving the problem (e.g., operating costs)?
a. Project planning matrix
b. Project charter
c. Value stream map
d. Performance diagram (P-Diagram)
See NOTES. Project Charter includes the What, When, Extent, and Impact of the problem. Project
Planning/Prioritization Matrix helps determine which projects in the pipeline to select to and
work on. Value Stream Map documents the actions to get a product/service to the customer.
PDiagram analyzes potential causes by documenting key process inputs and outputs.
2) Given the following statistical results, which of the following may be reasonably concluded?
a. No evidence to suggest data are not Normally Distributed
b. Data are skewed right
, Practice Exam
Page 2
c. Data are skewed left
d. Sample size is too low to conduct a Normality Test
See NOTES. Skewness value of 1.597 suggests that the distribution is not normally distributed (eliminate
answer A). A positive skew value suggested skewed right (answer B and eliminate answer C). Sample size
(N) = 50 and is large enough to conduct a normality test (eliminate answer D).
3) Which of the following statistics are displayed for the ‘box’ portion of a box plot?
a. Mean + 3 standard deviations
b. Median + 2 standard deviations
c. 1st Quartile, Median, and 3rd Quartile
d. Mean + 2 standard deviations
See NOTES. The box shows the 25th to 75th percentile (Quartile 1 to Quartile 3). The bottom line is the 1st
quartile, the middle line is the median, and the top line is the 3rd quartile.
4) What is the rolled yield of a 5-step serial process with the following yields for each step?
Step 1: 0.85; Step 2: 0.94; Step 3: 0.64; Step 4: 0.98; Step 5: 0.95
Assume each step is based on defective/not defective (Binary – Binomial).
a. 47.61%
b. 86.2%
c. 87.2%
d. 100%
Rolled Yield = 0.85*0.94*0.64*0.98*0.95 = 0.4761 = 47.61%
5) Suppose you inspect car doors on finished vehicles. For each door, you check for paint quality defects,
out-of-alignment areas of the door, and out-of-flush areas of the door between the front fender. If you
wish to visually show where on the door most of the defects are appearing, which of the following tools
would you most likely use?
a. Cause-Effect Diagram (Fishbone Diagram)
b. P-Diagram
c. Defect Location Check Sheet
d. Either (a) or (b)
, Practice Exam
Page 3
See NOTES. Defect Location Check Sheet shows visual location of issues. Cause-Effect Diagrams and
PDiagrams analyze potential causes.
6) A billing representative examines reasons for denial of payment after claims submission. A
check sheet is used to record the frequency of some common submittal problems. The data are
summarized in the following table.
Claim Defect Reason Frequency
Missing insurance number 15
Days of care wrong 10
Services provided incorrect 21
Referral information missing 2
Typo 4
Other 5
Total 57
Given the above table for denial of claims, what would be the cumulative relative frequency
for the category “missing insurance number” after performing a Pareto Analysis?
a. 63%
b. 44%
c. 26%
d. 80%
, Practice Exam
Page 4
7) Suppose you work for an office furniture manufacturer and you inspect outgoing products
(desks, credenza, etc.). Any given product may have multiple defects (1 or more per unit). Given
the following inspection data, which of the following would be most representative of the
current state of this process? (Assume that drawers cannot simultaneously have a gap that is ‘too
wide’ and ‘too narrow’ for a given manufactured unit and that Yield may be estimated using
DPU based on a Poisson distribution).
Gap Gap
Between Between
Excess Excess Drawers Drawers Missing
# Units Scratches Chips too wide too narrow Piece
Desk (w/two drawers) 200 5 4 3 6 2
Credenza (w/ 2 drawers) 190 7 2 1 0 3
File Cabinet (w/ 2 drawers) 210 9 1 2 6 2
Book Case 75 4 3 N/A N/A N/A
Total 675 25 10 6 12 7
N/A - not applicable
a. DPMO=3.4 (Yield = 99.99966%)
b. DPMO=17,778 (Yield = 1.8%)
c. DPMO=19,048 (Yield = 98%)
d. DPMO=23,529 (Yield = 91.5%)
The two ‘gap between drawer’ categories should be treated as a single opportunity because they
cannot both happen simultaneously. So, the first three furniture types have 4 defect
opportunities per unit: excess scratches, excess chips, gap between drawers, and missing piece.
Book cases only have 2 opportunities per unit: excess scratches, and excess chips.
Total Defects = 25 + 10 + 6 + 12 + 7 = 60
Total Opportunities = (200 * 4 per unit)+(190 * 4 per unit)+(210 * 4 per unit)+(75 * 2 per unit) =
2550
DPMO = Total # Defects / Total Opportunities x 1 million = * 1,000,000 = 23,529.4
Defect per Unit (DPU) = Total # Defects / Total # Units = = 0.08889
Yield (assuming Poisson) = Pr(K=0) = e-dpu = e-0.08889 = 0.91495 = 91.5%
8) For the above furniture problem, suppose you estimate the average cost to repair each of the
defect types (see last row in table below). Based on a Pareto Analysis and the primary objective
of a DMAIC project, which defect type should be addressed first?
