NORMAL DISTRIBUTIONS

NORMAL DISTRIBUTIONS

1. distribution is the most important and most widely used distribution in statistics. It is sometimes called the “bell curve,” although the tonal qualities of such a bell would be less than pleasing. It is also called the “Gaussian curve” after the mathematician Karl Friedrich Gauss. As you will see in the section on the history of the normal distribution, although Gauss played an important role in its history, de Moivre first discovered the normal distribution.

   • 1. Normal distributions are symmetric around their mean.
     • 2. The mean, median, and mode of a normal distribution are equal.
       • 3. The area under the normal curve is equal to 1.0.
         • 4. Normal distributions are denser in the center and less dense in the tails.
           • 5. Normal distributions are defined by two parameters, the mean (μ) and the standard deviation (σ).
             • 6. 68% of the area of a normal distribution is within one standard deviation of the mean.
               • 7. Approximately 95% of the area of a normal distribution is within two standard deviations of the mean.
   • As discussed in the introductory section, normal distributions do not necessarily have the same means and standard deviations. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.

2. Learning Objectives

   • 1. Name the person who discovered the normal distribution and state the problem he applied it to
     • 2. State the relationship between the normal and binomial distributions
       • 3. State who related the normal distribution to errors
         • 4. Describe briefly the central limit theorem
           • 5. State who was the first to prove the central limit theorem