# Six Sigma Black Belt Certification v6.1

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Exam contains 230 questions

A project that lacks a clear definition of its scope and boundaries runs the risk of:

• A. straying from the intended path
• B. trying to solve unrelated problems
• C. having difficulty in collecting baseline data
• D. suffering morale problems
• E. all the above
• F. none of the above

The primary metric for a project is reduced cost for process A .A consequential metric could be:

• A. reduced cycle time
• B. reduced scrap rate
• C. reduced set-up time
• D. all the above
• E. none of the above

The primary metric for a project is reduced cost for process A . Baseline data might include:

• A. current maintenance costs
• B. current selling price for the products or services output by process A
• C. current suggestions from stakeholders of process A
• D. all the above
• E. none of the above

According to the Central Limit Theorem:

• A. the median and the mean have the same value in a symmetric distribution
• B. the mode of a normal distribution is also the mean
• C. the mean of an exponential distribution is smaller than the median
• D. the mean, median and mode of a normal distribution all have the same value
• E. none of the above

The term “expected value” is closest to the term:

• A. median
• B. probabilistic model
• C. mean
• D. Markov value
• E. regressive value

A random sample is selected from a population of measurements. The mean of the sample is not equal to the mean of the population. This is due to:

• A. Type I error
• B. Type II error
• C. sampling error
• D. the population is not normal
• E. measurements were not exact

A population of size 1,000,000 has mean 42 and standard deviation 6. Sixty random samples, each of size 15 are selected. According to the Central Limit Theorem the distribution of the sixty sample means has a mean of approximately:

• A. 42
• B. 42/6
• C. 42/15
• D. 42/ 15
• E. none of the above

A population of size 1,000,000 has mean 42 and standard deviation 6. Sixty random samples, each of size 15 are selected. According to the Central Limit Theorem the distribution of the sixty sample means has a standard deviation of approximately:

• A. 6
• B. 6/42
• C. 6/15
• D. 6/ 15
• E. none of the above

A ____ from a sample is used to estimate a population _____. The two words that best fill these blanks are:

• A. item, value
• B. value, statistic
• C. statistic, parameter
• D. parameter, value
• E. parameter, statistic

Deming called the technique of studying a sample to gain understanding of the distribution of a population an enumerative study. His main objection to these studies was:

• A. they are too difficult to perform correctly
• B. they require extensive use of computers
• C. they assume a stable distribution
• D. random samples are expensive to obtain
• E. these studies have a high probability of Type II error

If the probability that an event will occur is 0.83, then the probability that the event will not occur is:

• A. 0.17
• B. 0.07
• C. 0.6889
• D. 1.20
• E. 83%

If the probability that event A occurs is 0.51, the probability that event B occurs is 0.64 and that probability that both A and B occur is 0.23 then:

• A. events A and B are complementary
• B. events A and B are mutually exclusive
• C. events A and B are supplementary
• D. events A and B are not mutually exclusive
• E. events A and B are statistically independent

If the probability that event A occurs is .51, the probability that event B occurs is .64 and events A and B are statistically independent then:

• A. A and B are mutually exclusive
• B. the probability that both A and B occur is 0.3264
• C. A and B can’t both occur
• D. the probability that A occurs is 1-(probability that B occurs)
• E. A and B have different standard deviations

A population is bimodal. One hundred samples of size 30 are randomly collected and the
100 sample means are calculated. The distribution of these sample means is:

• A. bimodal
• B. approximately exponential
• C. approximately Poisson
• D. approximately normal
• E. approximately uniform

A population is bimodal with a variance of 5.77. One hundred samples of size 30 are randomly collected and the 100 sample means are calculated. The standard deviation of these sample means is approximately:

• A. 5.77
• B. 2.40
• C. 1.05
• D. 0.44
• E. 0.19