Transcript Preview of 7.4 - Brookwood High School

7.4
Use Normal Distributions
7.3-7.4 HW Quiz: August 18
7.3-7.4 Quiz: August 20
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:
σ=1
standard
deviation
Vocabulary
• Standard Normal Distribution
Is the normal distribution with
mean 0 and standard deviation 1.
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.
P(x < x + σ)
P(x < x < x + 2σ)
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?
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.
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 3:
• Use the information about white oak trees from Example
2 to answer the following.
– 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)
– Now you need to use the Standard Normal Table
You Try:
•
In the following exercises, refer to
Example 2.
1. About what percent of white oak trees have
height between 83 feet and 90 feet.
2. Find the probability that a randomly
selected white oak tree has a height of at
most 85 feet.
Homework
P. 266
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