Unit 6 Section 5.1

5.1: Introduction to Normal Distributions and Standard Normal Distributions  A normal distribution is a continuous, symmetric, bell shaped distribution of a variable.

Properties of a Normal Distribution  Bell-shaped and symmetrical about the mean  The mean, median, and mode are the same value. These values are at the center of the curve  The total area under the curve is 1  The curve is continuous (no gaps)  The curve approaches but never touches the x-axis Section 5.1

 The values under curve indicate the proportion of area in each section.  i.e. the area between the mean and 1 standard deviation above or below the mean is = 34.14%.  Note : all areas are positive Section 5.1

Finding Areas Under the Standard Normal Distribution Curve  Step 1 : Draw a picture  Step 2 : Shade the area desired  Step 3 : Determine what z-values you will need to find the appropriate area.  Step 4 : Use Table 4 (pg A16-A17) to determine the area. Section 5.1

 Example 1 : Find the area under the standard normal distribution curve between z = 0 and z = 2.34 Section 5.1

 Example 2 : Find the area under the standard normal distribution curve between z = 0 and z = Section 5.1

 Example 3 : Find the area under the standard normal distribution curve to the right of z = 1.11 Section 5.1

 Example 4 : Find the area under the standard normal distribution curve to the left of z = Section 5.1

 Example 5 : Find the area under the standard normal distribution curve between z = 2.00 and z = 2.47 Section 5.1

 Example 6 : Find the area under the standard normal distribution curve between z = and z = Section 5.1

 Example 7 : Find the area under the standard normal distribution curve between z = 1.68 and z = Section 5.1

 Example 8 : Find the area under the standard normal distribution curve to the left of z = 1.99 Section 5.1

 Example 9 : Find the area under the standard normal distribution curve to the right of z = Section 5.1

 Example 10: Find the area under the standard normal distribution curve to the right of z = 2.43 and to the left of z = Section 5.1

Homework:  Pg 242 : 11 – 22, ODD  You must draw a picture and the shaded area for ODD Section 5.1