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USE NORMAL DISTRIBUTIONSSection 11.3
OBJECTIVES: Find normal probabilities
Interpret normal distributions
KEY VOCABULARY: Normal distribution Normal curve Standard Normal Distribution z-score
NORMAL DISTRIBUTIONS AND NORMAL CURVESA 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 and standard
deviation σ. For a randomly selected x-value from the distribution, find .
)2( xxxP
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?
#1: A NORMAL DISTRIBUTION HAS MEAN AND STANDARD DEVIATION . FIND THE INDICATED PROBABILITY FOR A RANDOMLY SELECTED X-VALUE FROM THE DISTRIBUTION.
x
)( xxP
#2: A NORMAL DISTRIBUTION HAS MEAN AND STANDARD DEVIATION . FIND THE INDICATED PROBABILITY FOR A RANDOMLY SELECTED X-VALUE FROM THE DISTRIBUTION.
x
)( xxP
#3: A NORMAL DISTRIBUTION HAS MEAN AND STANDARD DEVIATION . FIND THE INDICATED PROBABILITY FOR A RANDOMLY SELECTED X-VALUE FROM THE DISTRIBUTION.
x
)2( xxxP
#4: A NORMAL DISTRIBUTION HAS MEAN AND STANDARD DEVIATION . FIND THE INDICATED PROBABILITY FOR A RANDOMLY SELECTED X-VALUE FROM THE DISTRIBUTION.
x
)( xxxP
#5: A NORMAL DISTRIBUTION HAS MEAN AND STANDARD DEVIATION . FIND THE INDICATED PROBABILITY FOR A RANDOMLY SELECTED X-VALUE FROM THE DISTRIBUTION.
x
)3( xxP
#6: A NORMAL DISTRIBUTION HAS MEAN AND STANDARD DEVIATION . FIND THE INDICATED PROBABILITY FOR A RANDOMLY SELECTED X-VALUE FROM THE DISTRIBUTION.
x
)( xxP
STANDARD NORMAL DISTRIBUTIONThe 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
Page 759
)4.0( zP
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.Explain why it makes sense that . 5.0)0( zP
HOMEWORK ASSIGNMENTPage 760 #4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 32, 34