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Chapter 6.1 Normal Distributions. Distributions Normal Distribution A normal distribution is a continuous, bell-shaped distribution of a variable. Normal.

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Presentation on theme: "Chapter 6.1 Normal Distributions. Distributions Normal Distribution A normal distribution is a continuous, bell-shaped distribution of a variable. Normal."— Presentation transcript:

1 Chapter 6.1 Normal Distributions

2 Distributions

3 Normal Distribution A normal distribution is a continuous, bell-shaped distribution of a variable. Normal curves each have their own means and standard deviations

4 Properties of the 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%

5 Remember this? Normal Curve and Standard Deviation

6 Find the area under the curve for each of the following: 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

7 The standard normal distribution The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

8 z-score Recall that z-score, or standard score is:

9 Find area under the standard normal distribution curve 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

10 To the left: Find the are to the left of z=2.06

11 To the right Find the area to the right of z=-1.19

12 Between Find the area between z=+1.68 and z=-1.37

13 Find the following probabilities 1.P(z < 1.65) 2.P(z > 1.91) 3.P(0 < z < 2.32)

14 Find z-value Find the z-value such that the area under the standard normal distribution curve between 0 and the z value is 0.2123

15 Applying the Concepts Pg. 309 #1-10


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