Unit 6Section 5.1

5.1: Introduction to Normal Distributions and Standard Normal Distributions

A normal distribution is a continuous, symmetric, bell shaped distribution of a variable.

Properties of a Normal Distribution

Bell-shaped and symmetrical about the mean

The mean, median, and mode are the same value. These values are at the center of the curve

The total area under the curve is 1

The curve is continuous (no gaps)

The curve approaches but never touches the x-axis

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The values under curve indicate the proportion of area in each section.

i.e. the area between the mean and 1 standard deviation above or below the mean is 0.3414 = 34.14%.

Note: all areas are positive

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Finding Areas Under the Standard Normal Distribution Curve

Step 1: Draw a picture

Step 2: Shade the area desired

Step 3: Determine what z-values you will need to find the appropriate area.

Step 4: Use Table 4 (pg A16-A17) to determine the area.

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Example 1:

Find the area under the standard normal distribution curve between z = 0 and z = 2.34

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Example 2:

Find the area under the standard normal distribution curve between z = 0 and z = -1.75

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Example 3:

Find the area under the standard normal distribution curve to the right of z = 1.11

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Example 4:

Find the area under the standard normal distribution curve to the left of z = -1.93

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Example 5:

Find the area under the standard normal distribution curve between z = 2.00 and z = 2.47

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Example 6:

Find the area under the standard normal distribution curve between z = -2.48 and z = -0.83

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Example 7:

Find the area under the standard normal distribution curve between z = 1.68 and z = -1.37

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Example 8:

Find the area under the standard normal distribution curve to the left of z = 1.99

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Example 9:

Find the area under the standard normal distribution curve to the right of z = -1.16

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Example 10:

Find the area under the standard normal distribution curve to the right of z = 2.43 and to the left of z = -3.01

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Homework: Pg 242: 11 – 22, 23-35 ODD

You must draw a picture and the shaded area for 23-35 ODD

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