Download Business Statistics: A First Course, 3rd Edition

Continuous Probability
Distributions

Continuous Random Variable
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Continuous Probability Distribution
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Values from interval of numbers
Absence of gaps
Distribution of continuous random variable
Most Important Continuous Probability
Distribution

The normal distribution
© 2003 Prentice-Hall, Inc.
Chap 5-1
The Normal Distribution: Empirical Rule
68-95-99.7 Rule
 ~68% of the area
Lies within 1 std. dev.
 ~95% of the area
Lies within 2 std. dev.
 ~99.7% of the area
Lies within 3 std. dev.
From the mean

f(X)

Mean
Median
Mode
X
The Normal Distribution
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“Bell Shaped”
Symmetrical
Mean, Median and
Mode are Equal
Interquartile Range
Equals 1.33 s
Random Variable
has Infinite Range
f(X)

Mean
Median
Mode
X
Many Normal Distributions
There are an Infinite Number of Normal Distributions
Varying the Parameters s and , we obtain
Different Normal Distributions
Finding Probabilities
Probability is
the area under
the curve!
P c  X  d   ?
f(X)
c
© 2003 Prentice-Hall, Inc.
d
X
Chap 5-5
Normal Distribution in
Statcrunch
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Stat
Calculators
Normal:
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

Enter mean and standard deviation
Either solve a probability for a cumulative range
Or solve a cumulative range for a probability
© 2003 Prentice-Hall, Inc.
Chap 5-6
Assessing Normality


Not All Continuous Random Variables are
Normally Distributed
It is Important to Evaluate how Well the Data
Set Seems to be Adequately Approximated by
a Normal Distribution
© 2003 Prentice-Hall, Inc.
Chap 5-7
Assessing Normality

Construct Charts
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
(continued)
For small- or moderate-sized data sets, do stemand-leaf display and box-and-whisker plot look
symmetric?
For large data sets, does the histogram or polygon
appear bell-shaped?
Compute Descriptive Summary Measures
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
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Do the mean, median and mode have similar
values?
Is the interquartile range approximately 1.33 s?
Is the range approximately 6 s?
© 2003 Prentice-Hall, Inc.
Chap 5-8
Assessing Normality

Observe the Distribution of the Data Set
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(continued)
Do approximately
between mean 
Do approximately
between mean 
Do approximately
between mean 
68% of the observations lie
1 standard deviation?
4/5 of the observations lie
1.28 standard deviations?
95% of the observations lie
2 standard deviations?
Evaluate Normal Probability Plot

Do the points lie on or close to a straight line with
positive slope?
© 2003 Prentice-Hall, Inc.
Chap 5-9
Assessing Normality

(continued)
Normal Probability Plot
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Arrange Data into Ordered Array
Find Corresponding Standardized Normal Quantile
Values
Plot the Pairs of Points with Observed Data Values
on the Vertical Axis and the Standardized Normal
Quantile Values on the Horizontal Axis
Evaluate the Plot for Evidence of Linearity
© 2003 Prentice-Hall, Inc.
Chap 5-10