Transcript 7.4 (Purple) Use Normal Distributions

7.4
(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( x – σ < x < x )
4. P(x ≤ x – 3σ)
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 3.5 feet.
– About what percent of white oak trees have
heights between 86.5 feet and 93.5 feet?
Example Cont’d
– Find the probability that a randomly
selected white oak tree has a height of at
most 94 feet.
– You need to find the z-score (use the
formula)
Look at the
Standard
Normal Table
You Try:
•
For the following questions, refer to
Example 2.
1. About what percent of white oak trees have
heights less than 97 feet?
2. About what percent of white oak trees have
heights between 83 feet and 90 feet?
3. Find the probability that a randomly selected
white oak tree has a height of at most 85 feet.
Homework
• Review for Midterm
*Answers to the review book work is on my teacher page*
MIDTERM
TOMORROW!