1. Unit 4: Normal Distributions Part 3 Statistics

2. Focus Points Find the areas under the standard normal curve Find data from standard normal table

3. Standard Normal Distribution The standard normal distribution is a normal distribution with mean μ = 0 and standard deviation σ = 1. Any normal distribution of x values can be converted to the standard normal distribution by converting all x values to their corresponding z values. Finding the z score

4. Reading the Standard Normal Table For areas to the left of the specified z values, use the table entry directly. For areas to the right of a specified z value, look up the table entry and subtract from 1. For areas between two z values, z1 and z2 [where z1 < z2], subtract the table area for z1 from the table area from z2.

5. Guided Exercise #1 Find the area under the curve given the z values a) z 1.00 0.84134 1 - 0.84134=0.15866

6. Guided Exercise #1 Find the area under the curve given the z values b) z < 2.70 0.99653

7. Guided Exercise #1 Find the area under the curve given the z values c) 1.00 < z < 2.70 0.84134 0.99653 0.99653 - 0.84134 =.15519

8. Solving Problems with the Standard Normal Table 1. Find the z score 2. Notate whether less than or greater than 3. Use the table to get area 4. Convert into percentages

9. Guided Exercise #2 The weight of fawns between 1 and 5 months is normally distributed with mean μ = 27.2 kg with standard deviation σ = 4.3 kg. Let x be the weight of a fawn in kg’s. Use the standard normal table to find the percent of fawns that are a) Less than 30 kg Step 1: Find z scoreStep 2: Less than/Greater than z < 0.65

10. Cont. Step 3: Use the table.74215

11. Guided Exercise #2 The weight of fawns between 1 and 5 months is normally distributed with mean μ = 27.2 kg with standard deviation σ = 4.3 kg. Let x be the weight of a fawn in kg’s. Use the standard normal table to find the percent of fawns that are a) More than 26 kg Step 1: Find z scoreStep 2: Less than/Greater than z > - 0.28

12. Cont. Step 3: Use the table 0.389741 - 0.38974 = 0.61026

13. Guided Exercise #2 The weight of fawns between 1 and 5 months is normally distributed with mean μ = 27.2 kg with standard deviation σ = 4.3 kg. Let x be the weight of a fawn in kg’s. Use the standard normal table to find the percent of fawns that are a) Between 20 and 35 kg Step 1: Find z score Step 2: Less than/Greater than - 1.67 < z < 1.81

14. Step 3: Use the table Cont. 0.96485 - 0.04746 = 0.91749