This week and next week we will concentrate on the Normal distribution, also known as the Gaussian distribution. The graph of a Normal distribution is characterized by the familiar bell-shaped curve. It’s important for you to understand that there are many normal distributions–each taking its particular bell-shape based on its mean and standard deviation.
Understanding the properties of the normal distribution is absolutely critical as you begin to build the fundamental blocks of inferential statistics. The Normal distribution is commonly and frequently used in science, engineering, and the social science fields. Likewise understanding the Normal distribution is essential if you are to appreciate estimation, forecasting, and testing of hypotheses–all of which we will investigate in the ensuing weeks. Consequently, some claim that the Normal distribution is the most important distribution in all of statistics.
This week we continue our study of the normal distribution. By now I hope that you have familiarized yourself with the NORMDIST, and NORMSDIST functions in Excel. These functions are very easy to use–and are usually more accurate than using the standard normal table to solve problems.
Additionally, the NORMDIST and NORMINV functions eliminate the need to convert random variables that are normally distributed with a mean = f$displaystyle mu f$ and standard deviation = f$displaystyle sigma f$ to their corresponding z-scores. This business of transforming such random variables to their corresponding z-scores was certainly useful 25 years ago, before the NORMDIST and NORMINV functions came on scene. This was so, because computing probabilities associated with random variables having a normal distribution with mean = f$displaystyle mu f$ and standard deviation = f$displaystyle sigma f$ involved the calculation of some pretty complicated integrals to find the associated areas under the particular normal curve. Now, however, we have NORMDIST and NORMINV at our disposal and converting to z-scores is not usually necessary. So, give the Excel functions a try. They will simplify things for you.
You–and ultimately only you–are responsible for your learning. Others, of course, will help you, but others cannot carry you. That said, please seize the opportunity to learn the material we explore in our course. Naturally, reach out to me and others when you must. And, stay on task and maintain your pace as you make your way through the course.
To help understand Normal Probabilities, the Empirical Rule and how the bell-shaped distribution will look using a mean and a SD, I encourage you to review the PDF. This will also benefit you in the discussion this week AND on the Knowledge Check Homework and Tests in the Quizzes section. It will give you a good step by step guide to help answer the question in the discussion BUT you can also utilize and use these PDFs on the material in the course.
Week 4 Empirical Rule
Week 4 normal probabilities PDF
Here are additional PDFs that were created to help you with the Knowledge Check Homework and Tests in the Quizzes section and on the Lessons in the course. While they won’t be used to answer the questions in the discussion, they are just as useful and beneficial. I encourage you to review these ASAP!
Week 4 Exponential probabilities
Week 4 Uniform probabilities