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More on Normal Distributions

  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.)