2. 6.4 Standard Normal Distribution Objectives: By the end of this section, I will be able to… 1) Find areas under the standard normal curve, given a Z-value. 2) Find the standard normal Z-value, given an area.

3. The Standard Normal Curve It is a normal distribution with a mean of 0 and a standard deviation of 1 AREA = PROBABILITY

4. Standard Normal Curve

5. Three Cases for Finding Areas Finding areas to the LEFT of z. Finding areas to the RIGHT of z. Finding areas between two z values.

6. Case 1 1. Find the area to the left of z = 1.34 Step 1: Draw a normal curve Step 2: Mark the mean ( = 0) Step 3: Mark the z value(s) Step 4: Shade the area Step 5: Use the z table to find the area 0 1.34 0.9099

7. Case 2 1. Find the area to the right of z = -2.06. 0 -2.06 A = 0.0197 A = 1 - 0.0197 A = 0.9803

8. Case 3 2. Find the area between z = -1.06 and z = 2.38 in a standard normal curve. -1.06 2.38 0 A = 0.1446 A = 0.9913 A = 0.9913 – 0.1446A = 0.8467

9. Working Backwards 2. Now you are GIVEN the AREA and must find the z-score. z1z1 0 A = 0.87 Go to the chart and find the closest value to 0.87 z = 1.12 has an area of 0.8686 z = 1.13 has an area of 0.8708 Which is closer? z = 1.13

10. Working Backwards Find the standard normal z-value that has an area of 0.24 to the RIGHT of it. z1z1 0 A = 0.24 Find the area of the ? in order to find the missing z value. 1 – 0.24 z = 0.70 is A = 0.7580 z = 0.71 is A = 0.7611 z = 0.71 ? A = 0.76 Go to Chart A = 0.76

11. PRACTICE Page 293- 294 #6, 10, 16, 22, 28, ON A SEPARATE SHEET OF PAPER WITH A PARTNER. IT WILL BE GRADED. YOU MUST DRAW DIAGRAMS.