USE NORMAL DISTRIBUTIONS
Section 11.3
OBJECTIVES:

Find normal probabilities

Interpret normal distributions
KEY VOCABULARY:
Normal distribution
 Normal curve
 Standard Normal Distribution
 z-score

NORMAL DISTRIBUTIONS AND NORMAL
CURVES
A normal distribution is modeled by a bell-shaped
curve called a normal curve that is symmetric
about the mean
AREAS UNDER A NORMAL CURVE (PAGE
757)
EXAMPLE 1:
A normal distribution has mean
x and standard
deviation σ. For a randomly selected x-value
from the distribution,
.
P( x find
 2  x  x)
EXAMPLE 2:
The blood cholesterol readings for a group of women are
normally distribution with a mean of 172 mg/dl and a
standard deviation of 14 mg/dl.
a)
About what percent of the women have reading
between 158 and 186?
b)
Readings higher than 200 are considered
undesirable. About what percent of the readings are
undesirable?
x
#1: A NORMAL DISTRIBUTION HAS MEAN
AND
 . FIND THE INDICATED
STANDARD DEVIATION
PROBABILITY FOR A RANDOMLY SELECTED XVALUE FROM THE DISTRIBUTION.
P( x  x)
x
#2: A NORMAL DISTRIBUTION HAS MEAN
AND
 . FIND THE INDICATED
STANDARD DEVIATION
PROBABILITY FOR A RANDOMLY SELECTED XVALUE FROM THE DISTRIBUTION.
P( x  x)
x
#3: A NORMAL DISTRIBUTION HAS MEAN
AND
 . FIND THE INDICATED
STANDARD DEVIATION
PROBABILITY FOR A RANDOMLY SELECTED XVALUE FROM THE DISTRIBUTION.
P( x  x  x  2 )
x
#4: A NORMAL DISTRIBUTION HAS MEAN
AND
 . FIND THE INDICATED
STANDARD DEVIATION
PROBABILITY FOR A RANDOMLY SELECTED XVALUE FROM THE DISTRIBUTION.
P( x    x  x)
x
#5: A NORMAL DISTRIBUTION HAS MEAN
AND
 . FIND THE INDICATED
STANDARD DEVIATION
PROBABILITY FOR A RANDOMLY SELECTED XVALUE FROM THE DISTRIBUTION.
P ( x  x  3 )
x
#6: A NORMAL DISTRIBUTION HAS MEAN
AND
 . FIND THE INDICATED
STANDARD DEVIATION
PROBABILITY FOR A RANDOMLY SELECTED XVALUE FROM THE DISTRIBUTION.
P( x  x   )
STANDARD NORMAL DISTRIBUTION
The standard normal distribution is the normal
distribution with mean 0 and standard deviation 1.
The formula below can be used to transform x-values
into standard normal distribution.
The z-value for a particular x-value is called the z-score
and is the number of standard deviations the x-value
lies above or below the mean.
STANDARD NORMAL TABLE
P ( z  0 . 4 )
Page 759
EXAMPLE 3:
Scientist conducted aerial surveys of a seal
sanctuary and recorded the number x of seals
they observed during each survey. The numbers
of seals observed were normally distributed with
a mean of 73 seals and a standard deviation of
14.1 seals. Find the probability that at most 50
seals were observed during a survey.
#8: COMPLETE.
In Example 3, find the probability that at most 90
seals were observed during a survey.
#9: COMPLETE.
P( z  0)  0.5
Explain why it makes sense that
.
HOMEWORK ASSIGNMENT
Page 760 #4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 32,
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