More on Normal Distributions

First, this section talks about the history of the normal distribution and the central limit theorem and the relation of normal distributions to errors. Then, it discusses how to compute the area under the normal curve. It then moves on to the normal distribution, the area under the standard normal curve, and how to translate from non-standard normal to standard normal. Finally, it addresses how to compute (cumulative) binomial probabilities using normal approximations.


  1. The standard normal distribution is defined as a normal distribution with a mean of 0 and a standard deviation of 1.

  2. Z is equal to the number of standard deviations below or above the mean. Numbers below the mean have negative Z scores.

  3. 25 is 1.5 SDs above the mean: Z = (X - M)/SD = (25 - 16)/6 = 1.5

  4. Z = (X - M)/SD = (6 - 18)/5 = -2.40, Look at the table to see that the area below -2.40 is .0082. (This answer can also be found using the Java applet instead of the table.)