文档介绍：(Purple) Use Normal Distributions
Midterm: TOMORROW *Answers to the review book work is on my teacher page*
Statistics Quiz: Friday
Vocabulary
Normal Distribution
Is modeled by a bell-shaped curve
called a normal curve that is
symmetric about the mean.
The total area under the related curve is 1.
The percentage of the area covered by each standard deviation from the mean is shown in the graph. (on the next slide).
Graph of a Normal Curve: You need to know this!
Vocabulary
Standard Normal Distribution
Is the normal distribution with
mean 0 and standard deviation 1.
On p. 264 in your textbook
Formula
The formula below can be used to transform x-values from a normal distribution with mean x and standard deviation σ into z-values having a standard normal distribution.
On p. 264 in your textbook
Z-Value
The z-value for a particular x-value is called the z-score for the x-value and is the number of standard deviation the x-value lies above or below the mean x.
***To use the z-score you will need to look at the table that is on p. 296 in your textbook***
Example 1:
A normal distribution has mean x and standard deviation σ. Find the indicated probability for a randomly selected x-value from the distribution.
P(x > x + σ)
P(x < x < x + σ)
You Try:
A normal distribution has mean x and standard deviation σ. Find the indicated probability for a randomly selected x-value from the distribution.
1.
P( ≤)
x
x
2.
P( > )
x
x
3.
P( –σ< x < )
x
x
4.
P(x ≤– 3σ)
x
Example 2:
The heights (in feet) of fully grown white oak trees are normally distributed with a mean of 90 feet and a standard deviation of feet.
About what percent of white oak trees have heights between feet and feet?