# Six Sigma Black Belt: Probability and Probability Distributions

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Organizations need to make inferences about a population from sample data, and understanding how to calculate the probability that an event will occur is crucial to making those inferences. In a Six Sigma context, it is often important to calculate the likelihood that a combination of events or that an ordered combination of events will occur. Understanding probabilities can provide Black Belts with the tools to make predictions about events or event combinations. To make accurate inferences about a population from the sample data collected in the Measure stage, Black Belts must also be familiar with the characteristics of various probability distributions, and their suitability for different types of data. Understanding the behavior of probability distributions allows the Black Belts to find the probability that values will be found within a given range, and thus to provide information on the variation in the organization's processes and products. This course provides Black Belts with basic information on probabilities and probability distributions, from the frequently used normal, Poisson, and binomial distributions, to the more specialized hypergeometric, Weibull, bivariate, exponential, and lognormal, as well as the distributions that test hypothesis and set confidence intervals: Chi-square, Student's t, and F distributions. When chosen appropriately to represent the data, these distributions will provide information on process and product variation, and support subsequent inferences based on sample data. This course is aligned with the ASQ Certified Six Sigma Black Belt certification exam and is designed to assist learners as part of their exam preparation. It builds on foundational knowledge that is taught in SkillSoft's ASQ-aligned Green Belt curriculum.

## WHAT YOU WILL LEARN

• discover the key concepts covered in this course calculate the probability of compound events in a given scenario use the appropriate formula to calculate the number of combinations or permutations in a given scenario identify equivalent approximations and conditions under which they hold true choose the appropriate discrete distribution for a given study recognize the characteristics and applications of lognormal, exponential, Weibull, and bivariate distributions choose the most suitable continuous probability distribution to use for a given scenario
• choose the appropriate distribution formula and use it to find probability, for a given scenario use the Z-score formula and normalized Z-table to calculate cumulative probability of a value, in a given scenario calculate the mean and standard deviation for binomial data recognize whether or not the hypergeometric distribution should be used and why, in a given scenario calculate probability using the hypergeometric distribution formula match Chi-square, Student's t-distribution, and F distribution to descriptions of when they are typically applied

## IN THIS COURSE

• 1.
Six Sigma Black Belt: Probability and Probability Distributions
• 2.
Probability, Combinations, and Permutations
• 3.
Discrete Variable Probability Distributions
• 4.
Continuous Variable Probability Distributions
• 5.
Normal and Poisson Distributions
• 6.
Binomial and Hypergeometric Distributions
• 7.
Chi-square, Student's t, and F Distributions

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