Transcript Chapter 6.1
Chapter 6.1 Normal Distributions Distributions • A normal distribution is a continuous, bell-shaped distribution of a variable. • Normal curves each have their own means and standard deviations Normal Distribution 1. Bell-shaped 2. The mean, median, and mode are equal and are located at the center of the distribution. 3. Unimodal 4. Symmetric about the mean 5. Continuous 6. Never touches the x-axis 7. Total area under the curve is 1.00 or 100% Properties of the Normal Distribution Normal Curve and Standard Deviation Remember this? 1. Area to the left of the mean 2. Area to the left of one standard deviation below the mean 3. Area to the right of two standard deviations above the mean Find the area under the curve for each of the following: • The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. The standard normal distribution • Recall that z-score, or standard score is: z X z-score Reading the table 1. Find the area for a z-score of 1.39 2. Find the area for a z-score of -0.25 3. Find the z-score for an area of .6293 4. Find the z-score for an area of .0012 Find area under the standard normal distribution curve • Find the are to the left of z=2.06 To the left: • Find the area to the right of z=-1.19 To the right • Find the area between z=+1.68 and z=-1.37 Between 1. P(z < 1.65) 2. P(z > 1.91) 3. P(0 < z < 2.32) Find the following probabilities • Find the z-value such that the area under the standard normal distribution curve between 0 and the z value is 0.2123 Find z-value • Pg. 309 #1-10 Applying the Concepts