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