1. Note: Normal Distribution Many sets of data collected in nature and other situations fit what is called a normal distribution. This means the data would fit a bell shaped curve where most of the values are clustered around the mean and a few are extreme values. Normally distributed data is described by giving the mean (middle value) and the standard deviation (measure of spread).

2. Example: If we measured the heights of all year 12 pupils we would find that they are normally distributed.  z

3. The probability of a data value being between two given values on the horizontal axis is given by the area under the curve, between those two values. Properties of the curve: It is symmetric about 0, the mean The total area under the curve is 1 The area under the curve to the left (or right) of zero is 0.5

4. The standard normal distribution has a mean of 0 and a standard deviation of 1.  = 1

5. Example 1: Find P (0 < Z < 1.478) = Calculator Instructions: MENU STAT DIST NORM Ncd Lower Upper   0 1.478 1 0 0.430296

6. Example 2: Find P (Z < -1.672) = Calculator Instructions: MENU STAT DIST NORM Ncd Lower Upper   -1000 -1.672 1 0 0.047262

7. Example 3: Find P (-1.25 < Z < 1.035) = Calculator Instructions: MENU STAT DIST NORM Ncd Lower Upper   -1.25 1.035 1 0 0.744016

8. Exercises : NuLake Page 31 - 34