Statistics chapter 6

Normal distribution

A continuous probability distribution for a random variable, x The graph of a normal distribution is called the normal curve

Continuous random variable

Has an infinite number of possible values that can be represented by an interval on the number line

the standard deviation describes

The standard deviation describes the spread of the data.

z score info

When calculating a z Score, round to 2 decimal places. If a z-score is halfway between two values in the table, round to 3 decimal places For a z-score less than -3.49, use 0.0000 to approximate the area. For a z-score greater than 3.49, use 1.0000 to approximate the area.

x score formula

x= zσ +μ

z-score formula

z=value-mean/standard deviation x-μ/ σ.

mean gives the location of....

The mean gives the location of the line of symmetry

Properties of a Normal distribution

The mean, median, and mode are equal. The normal curve is bell-shaped and is symmetric about the mean. The total area under the normal curve is equal to 1. The normal curve approaches, but never touches, the x-axis as it extends farther and farther away from the mean. Between μ - σ and μ + σ (in the center of the curve), the graph curves downward. The graph curves upward to the left of μ - σ and to the right of μ + σ. The points at which the curve changes from curving upward to curving downward are called the inflection points, or transition points.