continuous probability distributions introduction to business statistics, 5e kvanli/guynes/pavur...
Post on 20-Dec-2015
218 views
TRANSCRIPT
Continuous Probability Distributions
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Probability for aContinuous Random Variable
Figure 6.1Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Properties of aNormal Distribution
• Continuous Random Variable
• Symmetrical in shape (Bell shaped)
• The probability of any given range of numbers is represented by the area under the curve for that range.
• Probabilities for all normal distributions are determined using the Standard Normal Distribution.Introduction to
Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Probability Density Function for Normal Distribution
ex
xf )(2
1)(
2
21
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.2
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.3
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.4
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.5
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.6
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Determining the Probability for a Standard Normal Random Variable
• Figures 6.10-6.13
• P(- Z 1.62) = .5 + .4474 = .9474
• P(Z > 1.62) = 1 - P(- Z 1.62) =1 - .9474 = .0526
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.10
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.11
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Determining the probability of any Normal Random Variable
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Fig 6.20
Interpreting Z
• Example 6.2 Z = - 0.8 means that the value 360 is .8 standard deviations below the mean.
• A positive value of Z designates how may standard deviations () X is to the right of the mean ().
• A negative value of Z designates how may standard deviations () X is to the left of the mean ().
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Example 6.5
Referring to Example 6.2, after how many hours will 80% of the Evergol bulbs burn out?
P(Z < .84) = .5 + .2995 =
.7995 .8
Figure 6.26
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.26
44242400
42)84(.50400
84.50
400
o
o
o
x
x
xZ
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Continuous Uniform Distribution
• The probability of a given range of values is proportional to the width of the range.
• Distribution Mean:
• Standard Deviation:
a b
2
b– a
12Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.35
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.36
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Exponential Distribution
Applications:
• Time between arrivals to a queue (e.g. time between people arriving at a line to check out in a department store. (People, machines, or telephone calls may wait in a queue)
• Lifetime of components in a machineIntroduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Mean and Standard Deviation
Mean:
Standard Deviation:
P(Xx0 )1–e–Ax0 for x0 0
where A1/ ,
= 1A
and
1A
.Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Figure 6.39
P(Xx0 ) 1 – e– Ax0 for x0 0
where A1/ , =1
A, and 1
A.Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing