chapter 6.1 normal distributions. distributions normal distribution a normal distribution is a...

Chapter 6.1Normal Distributions

Distributions

Normal Distribution

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

• Normal curves each have their own means and standard deviations

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%

Remember this?

Normal Curve and Standard Deviation

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

The standard normal distribution

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

z-score

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

X

z

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

To the left:

• Find the are to the left of z=2.06

To the right

• Find the area to the right of z=-1.19

Between

• Find the area between z=+1.68 and z=-1.37

Find the following probabilities

1. P(z < 1.65)

2. P(z > 1.91)

3. P(0 < z < 2.32)

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

Applying the Concepts

• Pg. 309 #1-10