# Six Sigma Advanced Define and Measure Phas Answer

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## Week- 2

### Process Analysis and Documentation Graded Quiz

1.
Question 1
Mapping a process means involving those with the
most knowledge of how it works. This
would be:

1 point

• process designers
• customers
• workers who use the process
• managers and supervisors

2.
Question 2
The numbering system for procedures is important
for what reason?

1 point

• Compliance
• Productivity
• Quality
• Reference

3.
Question 3
Every task must have work instructions.

1 point

• True
• False

4.
Question 4
Work instructions are mostly useful in most types
of organizations, not just manufacturing.

1 point

• True
• False

5.
Question 5
Work instructions are often written,
but they may be supplemented, or in some cases replaced by other methods

1 point

• True
• False

6.
Question 6
CEDAC is a modified Cause and Effect diagram.

1 point

• True
• False

7.
Question 7
A Cause and Effect Diagram will lead
the team to the positive identification of root cause.

1 point

• True
• False

8.
Question 8
CEDAC information should be protected and kept
confidential.

1 point

• True
• False

9.
Question 9
A Pareto chart uses only discrete data.

1 point

• True
• False

10.
Question 10
A prioritization matrix provides a quantitative
method for making a decision, so you don’t have to rely on the judgment of the
team.

1 point

• True
• False

## Week- 3

### Probability and Statistics – pt1 Graded Quiz

1.
Question 1
What is the term for a collection of outcomes
from a probability experiment?

1 point

Sample space

Disjoint

Event

Probability

2.
Question 2
Which of the following could NOT be a
probability?

1 point

1.2

4/5

80%

1

3.
Question 3
Suppose the probability of having no defects in
the next lot that you sample is 0.05.
What is the probability that there WILL be at least one defect in the
next lot you sample?

1 point

0.05

0.95

0.10

1

4.
Question 4
True or false: The following two events are disjoint/mutually
exclusive?

Sitting directly to the left of someone on
the airplane: whose first name starts with an A; someone whose first name
starts with a vowel.

1 point

True

False

5.
Question 5
What is the term for two events that cannot
occur simultaneously?

1 point

Independent

Intertwined

Disjoint

Passive

6.
Question 6
True or false: The following two events are
independent?

Sitting directly to the left of someone on
the airplane: whose first name starts with an A; someone whose first name starts
with a vowel.

1 point

True

False

7.
Question 7
Which formula below is appropriate to use for
the addition rule if the two events are not disjoint?

1 point

P(B|A) = P(A&B) / P(A)

P(A or B) = P(A) + P(B)

P(A or B) = P(A) + P(B) – P(A&B)

P(A and B) = P(A) X P(B|A)

8.
Question 8
The probability that the cafeteria is serving
pasta for the hot lunch today is 0.2, pizza is 0.3, chicken is 0.1, and soup is
0.4. You like pasta and chicken. What is the probability that you will like
lunch today?

1 point

0.5

0.1

0.3

1.0

9.
Question 9
In your manufacturing plant, 50% of the
employees are able to operate the drill press, 70% are able to operate the CNC,
and 30% can operate both. What is the
probability that an employee can operate the CNC, given that they can operate
the drill press? Please round your answer to the nearest hundredth.

1 point

0.60

0.43

0.90

0.70

10.
Question 10
Consider a batch of raw materials, containing 5
defective and 20 good items. Suppose that two of the items are quality tested
without replacement. What is the probability that both items tested are good?
Please round your answer to the nearest hundredth.

1 point

0.50

0.80

0.64

0.63

## Week- 4

### Probability and Statistics – pt2 Graded Quiz

1.
Question 1
How many ways can the letters of the word “Word”
be arranged?

1 point

16

24

1

12

2.
Question 2
If you are going to the grocery store to pick up
3 pints of ice cream for your family and there are 15 choices, how many
different groups of 3 pints can you choose?
(Assume that you will choose 3 different types without duplication)

1 point

15

45

2730

455

3.
Question 3
When is the variance of the sampling
distribution of means equal to the variance of the population from which the
samples were drawn divided by the size of the samples?

1 point

Only when the original distribution is binomial

Always

Only when our original distribution is normally distributed or our sample size is large enough

This only happens by chance.

4.
Question 4
Which of the following is NOT part of the
Central Limit Theorem?

1 point

The mean of the sampling distribution of means is equal to the mean of the population from which the samples were drawn .

The variance of the sampling distribution of means is equal to the variance of the population from which the samples were drawn divided by the size of the samples.

If the original distribution is normally distributed the sampling distribution of the means will also be normal.

All of the above are part of the CLT

5.
Question 5
True or false, the central limit theorem tells
us that a sample mean is a fair, also called unbiased, estimate of the
population mean.

1 point

True

False

6.
Question 6
If the population standard deviation is 4 and you have a sample of size 25, what is the standard error?

1 point

4

0.16

0.8

0.4

7.
Question 7
Suppose finish times of employment applications for a temp agency follow a triangular distribution with known standard deviation of 1.5 minutes. You take a sample of size 36 and obtained a mean finish time of 8.2 minutes. What is a 95% confidence interval for the mean finish time?

1 point

0.25

(7.71,8.69)

(6.7,9.7)

This problem cannot be solved because the original distribution is triangular rather than normal

8.
Question 8
You have received a lot of 100 items from your
supplies and are going to randomly select 5 of them for quality testing to
determine if you will accept the lot. If you find more than 1 defect, you will
reject the lot. What is the *sample* in
that situation?

1 point

Everything the supplier has ever produced

The lot of 100 items

The 1 defect

The 5 items selected for testing

9.
Question 9
Suppose some election polling is done to predict
the outcome of the presidential election in the state of Georgia. 1000 likely voters are polled. What is the population in that situation?

1 point

The percentage of the voters polled who will vote Republican

All likely voters in Georgia

All US voters

The 1000 likely voters polled

10.
Question 10
In a statistical experiment, what does s represent?

1 point

The population mean

The sample standard deviation

The sample mean

The population standard deviation

11.
Question 11
A value, such as the mean, calculated from
population data is called a:

1 point

Statistic

Permutation

Parameter

Anomaly

12.
Question 12
When performing an analytical study, which of
the following would seldom be known?

1 point

The sample standard deviation

The degrees of freedom

The sample statistic

The true population parameter

## Week- 5

### Statistical Distributions Graded Quiz

1.
Question 1
1.
Which of the images below is left-skewed?

1 point 2.
Question 2
Which of the following is NOT a requirement to
model with the binomial distribution?

1 point

Exactly two possible states for the random variable

A constant probability of success between trials

A predetermined number of trials

A continuous random variable

3.
Question 3
A recent survey found that 7% of your suppliers
are not pleased with the terms of your contracts. If you randomly meet with 10 of your
suppliers, what is the probability that at least one of them is one that is not
pleased with the terms of the contracts?

1 point

0.364

0.516

0.700

0.484

4.
Question 4
Which of the following could be modeled with the
Poisson distribution?

1 point

The number of times you flip a fair coin before getting 3 heads

The probability of exactly 1 defect in 200 square meters of fabric

The probability of exactly 1 defect in the next 200 items you sample.

The probability of getting exactly 12 odd numbers when rolling a fair die 20 times.

5.
Question 5
The average number of flaws in bolts of fabric
that you are producing is 0.36. The
standard deviation of this Poisson distribution is…

1 point

Unable to be determined from the information given

0.64

0.36

0.6

6.
Question 6
Suppose that defects occur at a rate of 0.05 per
linear meter in tile trim manufacturing.
What is the probability that there are no more than 1 defects in the next
50 linear meters?

1 point

2.5

0.21

0.05

0.29

7.
Question 7
The tread life of a particular brand of tire is
a random variable best described by a normal distribution with mean of 65,000
miles and a standard deviation of 2900 miles.
What is the probability that a randomly selected tire will last less
than 64,000 miles?

1 point

0

0.365

0.634

0.5

8.
Question 8
Suppose
the length of time it takes students to complete an exam question follows a
normal distribution with a mean of 5.0 minutes and a standard deviation of 1.0
minute. Find the probability that a
randomly selected student will take between 2.5 and 4.5 minutes to complete the
question.

1 point

0.309

0.302

0.006

0.698

9.
Question 9
Which of the following is a practical use of the
Chi-square distribution?

1 point

Hypothesis tests for two population variances

Hypothesis tests for one population variance

Hypothesis tests for one mean when the population standard deviation is unknown

Hypothesis tests for one population proportion

10.
Question 10
Which of the following is an application of the
t-distribution?

1 point

Hypothesis tests for multiple proportions

Hypothesis tests for one population variance

Hypothesis tests for two population variances

Hypothesis tests for one mean when the population standard deviation is unknown

11.
Question 11
Which of the following distributions has their
axis starting at 0?

1 point

F

Regression

Normal

T

12.
Question 12
Which distribution is not affected by degrees of
freedom?

1 point

Chi-square

F

Normal

T

## Week- 6

### Collecting and Summarizing Data Graded Quiz

1.
Question 1
Given the following dataset. Indicate the median.

2.5, 5.1,
4.4, 6.3, 3.1, 8.5, 4.5, 7.7, 2.5

1 point

4.5

6.3

7.7

2.5

2.
Question 2
Given the following dataset.
Indicate the range.

2.5, 5.1, 4.4, 6.3, 3.1, 8.5, 4.5, 7.7, 2.5

1 point

5.2

5.4

6

3.8

3.
Question 3
Why would you want to randomize
your selection of sample data elements?

1 point

To achieve the results you are looking for

To avoid bias that could affect the study’s outcome

No reason to randomize, just pick who you want in your study

To achieve a high variance

4.
Question 4
Ways to
graphically display your data is included below, which method does NOT belong?

1 point

Stem-and-Leaf plots

Run Charts and Boxplots

Scatter diagrams

Random Number Table

5.
Question 5
Which of
the following graphical means shows continuous data?

1 point

A histogram

A tally sheet.

A run chart

A boxplot

6.
Question 6
A
scatter diagram is used to plot gas mileage versus the weight of a car. What would you expect to see if you placed a
line through the data points?

1 point

No correlation at all, the data points are randomly spaced out.

A decreasing slope.

An odd U shape.

An increasing slope.

7.
Question 7
Calculate Q1
from this dataset: 45, 13, 15, 34, 23,
38, 11

1 point

28.5

14

11

38

8.
Question 8
Calculate
IQR when Q1 = 10, Q2 = 20, and Q3 = 25

1 point

5

25

10

15

9.
Question 9
A Stem-and-Leaf plot will
help you indicate the mode of the dataset

1 point

True

False

10.
Question 10
Which value
does not belong in the calculation of a boxplot?

1 point

Range

Q1, Q2, and Q3

IQR, Max, and UL

LL, Min

### Measuring System Analysis Graded Quiz

1.
Question 1
Before you
begin your GR&R Study, the need to calibrate an instrument could be due to:

1 point

There is really no need to calibrate an instrument.

Factors such as humidity, temperature, or wear

2.
Question 2
Is it repeatability
or reproducibility, when one operator measures the same characteristics
of the same products using the same gage?

1 point

Reproducibility

Repeatability

3.
Question 3
Which statement is not a
characteristic of a Measurement System?

1 point

Detecting any changes in the process

Measurement systems are not considered in quality analysis

Capture the correct data

Detect the source of the measurement error

4.
Question 4
Which is not a source of measurement
variation?

1 point

The measuring device itself

The speed of the conveyor belt

Environmental sources such as humidity and temperature.

The operator or inspector conducting the measurements

5.
Question 5
What is your criteria to recruit a
study “appraiser”?

1 point

No criteria needed, just randomly pick anybody

Someone who is new to the part or process

Someone in your engineering department

Someone who measures parts during a normal production day.

6.
Question 6
In a measurement system, what is
Repeatability precision?

1 point

Has nothing to do with variation

The variation in measurement means when the same gage is used by the same operator

The variation in measurement averages when the same gage is used by different operators

Has nothing to do with the gage operator

7.
Question 7
The %GRR of the total variation is
24% and the %GRR of Tolerance is 17.5%, using Average and Range method what
conclusion can we draw?

1 point

The measurement system is marginal

The measurement system is not acceptable

The measurement system is acceptable

Must be separated into individual R&R values to be sure

## Week- 7

### Process and Performance Capability Graded Quiz

1.
Question 1
What should you
do next after you collect 20-25 sets of part samples in a Process Capability
Study?

1 point

Next, calculate R

Next, determine your subgroup sample size

Next, calculate the average for each subset of samples

Next, determine the range of the entire 60-90 data points collected

2.
Question 2
A control chart
is used to:

1 point

Determine causes of process variation

Detect non-random variation in processes

Determine if defective parts are being produced

Measure process capability

3.
Question 3
Your X-bar and R control chart has
shown in-control for a long time. You
notice that the last 50 samples plotted are all very near the centerline,
within 1 sigma. What does this indicate?

1 point

The process standard deviation has decreased during the last 50 samples

An undesirable situation has occurred

The process standard deviation has increased significantly

Stop the process

4.
Question 4
The six sigma project team is led
by a green belt. The current activity is
to develop a control plan. Who is best
prepared to develop this plan?

1 point

The project lead

The green belt

The inspector

The production supervisor

5.
Question 5
For the last 10 samples plotted,
your control chart is showing a steady decrease in your plots from within 1
sigma to the LCL. What is happening?

1 point

Plots are fluctuating on both sides of the centerline

A cyclical event is occurring

A trend is occurring.

No problem, the plots indicate in-control

6.
Question 6
When analyzing process capability,
if Cp equals Cpk, what does this indicate?

1 point

The process is completely out-of-control and not capable

Impossible because Cpk cannot equal Cp

Cp cannot change if Cpk changes

The process is perfectly centered

7.
Question 7
What is the typical corrective
action to take when a control chart shows cyclical signs?

1 point

Check your control limits and investigate material changes

Do nothing, everything is fine

Eliminate over-adjustments by the operator

Control the physical environment, service equipment, rotate operators, or sharpen tools

8.
Question 8
If X-double bar = 32 and R-bar
equals 10, what is UCLx-bar?
(A2 = 1.02, D4=2.57)

1 point

25.70

0

21.18

42.20

### Exploratory Data Analysis Graded Quiz

1.
Question 1
Identify the
major variation classifications specifically addressed in multi-vari studies?

1 point

Cylinder, batch, flat

Piece-to-piece, batch-to-batch, within piece

Temporal, top to bottom, side to side

Positional, cyclical, temporal

2.
Question 2
If you are studying the relationship between the number of hours of
overtime assigned at your facility and the number of defects in your product,
what would the INDEPENDENT variable be?

1 point

Hours of overtime assigned

Number of defects in your product

Both the hours of overtime assigned and the number of defects in your product

Neither the hours of overtime assigned nor the number of defects in your product

3.
Question 3
If
a scatter diagram is created plotting vegetable garden square footage vs. crop
yield, what would you expect the shape of the resulting plot to show?

1 point

Positive correlation

No correlation

Negative correlation

Circular correlation

4.
Question 4
Which
of the following statements are true about correlation?

1 point

r can range from -1 to 1

The correlation coefficient can only range from 0 to +1

The lower the correlation coefficient is, the weaker the correlation is

A positive correlation coefficient means that as the independent variable decreases, the dependent variable increases

5.
Question 5
What
is the method used to find the equation of the regression line called?

1 point

Perfect square method

Least squares method

Statistical analysis method

Normal distribution method

6.
Question 6
A
scatter plot in which the plotted points are clustered approximately into a
straight line from the top left to the bottom right of the graph is displaying
which of the following:

1 point

Negative correlation

Positive correlation

No correlation

Bimodal correlation

7.
Question 7
In
the equation for basic linear regression, what does the term “b” represent?

1 point

The slope of the line

The x intercept

The y intercept

The error

8.
Question 8
You
collect sample data to calculate the relationship between age of the
manufacturing equipment at your facility and the hours of downtime of that
equipment. Using data ranging from 0.5 years old to 20 years old for the
equipment, you obtain the regression equation for annual hours of downtime of
y=10+0.5x with a high correlation coefficient. How many hours of downtime would
you predict for equipment that is 8 years old? (Round to the nearest 10th
of a year)

1 point

14.0

8.0

4.0

You cannot use this regression equation to answer the
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