Download 5.1-guided-notes - Bryant Middle School

Statistics
5.1: Introduction to Normal Distributions and Standard Normal Distributions
Objective 1: I can interpret graphs of normal probability distributions.
In chapter 4 we looked at discrete probability distributions. In chapter 5, we are going to focus
on a very important ___________________ probability distribution, called the ______________
distribution. Normal distributions can be used to model many types of data sets. For example,
lifetime of tv sets, housing costs, and blood pressure measurements are all normally distributed
variables.
Properties of a Normal Distribution
A normal distribution is a ________________ probability distribution for a random variable x.
The graph of a normal distribution is called a ___________ curve. A normal distribution has the
following properties:
1)
2)
3)
4)
The normal curve looks like:
A normal distribution can have any ________ and any positive __________________________.
These two parameters, _____ and _____, completely determine the shape of the normal curve.
The mean gives the location of the ___________________________ and the SD describes how
much the data are _____________________.
Which two curves above have the same mean? __________
Which two curves above have the same SD? ___________
Example 1, pg 241
TIY 1:
Consider the normal curves shown below. Which normal curve has the greatest mean? _______
Which normal curve has the greatest SD? _______ Explain.
Ex 2:
TIY 2:
Objective 2: I can find areas under the standard normal distribution.
There are many normal distributions—weight of newborn babies, height of adult males, IQ
scores, etc. But there is only ONE ________________________________________. In chapter
2, we you learned that a z-score is a measure of position that indicates the number of standard
deviations a value lies from the mean. We used the formula below to transform any x-value in
that data set into a standard score.
Read paragraphs on page 243 below this diagram.
So basically, we can now use a table in the back of the book to find the area under the normal
curve for ANY z-score, not just -3, -2, -1, 0, 1, 2, 3 like we did in Chapter 2 using the Empirical
Rule.
Properties of the Standard Normal Distribution:
1)
2)
3)
4)
Ex 3: Using the Standard Normal Table (pages ______ and ______ in the orange section)
a) Find the cumulative area that corresponds to a z-score of 1.15
b) Find the cumulative area that corresponds to a z-score of -0.24.
TIY 3:
a) Find the area under the curve to the left of a z-score of -2.19.
b) Find the area under the curve to the left of a z-score of 2.17.
FINDING AREAS UNDER THE STANDARD NORMAL CURVE (pg 245)
1) The area in the table is the area to the ________ of any z-score from ______ to ______.
What is the area to the left of a z-score of -4 or smaller? ______
What is the area to the left of a z-score 4 or larger? ______
2) To find the area to the right of any z-score, find the area to the _______ of the z-score.
Then _____________________________.
What is the area to the right of a z-score of -4 or smaller? ______
What is the area to the right of a z-score 4 or larger? ______
3) To find the area between two z-scores, find the area to the _______ of each z-score.
Then __________________________________.
Ex 4: Finding area under the standard normal curve.
a) Find the area to the left of z = -0.99
b) Find the area to the right of z = 2.13.
Ex 5: Finding area under the standard normal curve.
a) Find the area to the right of z = 1.06
b) Find the area to the right of z = -2.16.
Ex 6: Find each area under the standard normal curve.
a) Between z = -1.5 and z = 1.25.
b) Between z = -2.16 and z = -1.35.
c) Between 0.19 and 2.87