Unit 4: Normal Distributions Part 3 Statistics

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

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

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.

Guided Exercise #1 Find the area under the curve given the z values a) z =

Guided Exercise #1 Find the area under the curve given the z values b) z <

Guided Exercise #1 Find the area under the curve given the z values c) 1.00 < z < =.15519

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

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

Cont. Step 3: Use the table.74215

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 >

Cont. Step 3: Use the table =

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 < z < 1.81

Step 3: Use the table Cont =