prob and stat chapter 6.2

1

A normal distribution curve is bell-shaped

3

A normal distribution curve is unimodal

7

The total area under the normal distribution curve is equal to 1.00 or 100%

normal distribution

is a continuous, symmetric, bell-shaped distribution of a variable

the standard normal distribution

is a normal distribution with a mean of 0 and a SD of 1

symmetric distributions

when the data values are evenly distributed about the mean

positively or right skewed distributions

when the majority of the data values fall to the left off the mean

negatively or left skewed distributions

when the majority of the data values fall to the right of the mean

Summary of the Properties of the Theoretical Normal Distribution

1. A normal distribution curve is bell-shaped 2. The mean, median and mode are equal and are located at the center of the distribution 3. A normal distribution curve is unimodal 4. The curve is symmetric about the mean - meaning the shape is the same on both sides of a vertical line passing through the center 5. The curve is continuous - there are no gaps or holes. For each value of X there is a corresponding value of Y. 6. The curve never touches the x-axis. 7. The total area under the normal distribution curve is equal to 1.00 or 100%. 8. The area under the part of the normal curve that lies within 1 SD of the mean is approx. 68%, within 2 SDs of the mean is approx. 95%, within 3 SDs of the mean is approx. 99.7%.

8

The area under the part of the normal curve that lies within 1 SD of the mean is approx. 68%, within 2 SDs of the mean is approx. 95%, within 3 SDs of the mean is approx. 99.7%

5

The curve is continuous - there are no gaps or holes. For each value of X there is a corresponding value of Y

4

The curve is symmetric about the mean - meaning the shape is the same on both sides of a vertical line passing through the center

6

The curve never touches the x-axis

2

The mean, median and mode are equal and are located at the center of the distribution