5.2
The Sampling Distribution of a Sample Mean
Figure 5.8
•averages are less variable than individual observations
•averages are more normal than individual observations
The mean and standard deviation of
x
x
= mean of sample
μ
= mean of population
σ
2
=
population variance
select an SRS of size n from a population and measure variable X on each individual in sample
the n measurements are values of n random variables X
1
, X
2
…
X
n
•X
i
is measurement on one individual selected at random from population then X
i
has the
distribution of the population
•if population is large relative to the size of the sample X
1
, X
2
…
X
n
considered independent
Mean and standard deviation of a sample mean
Let
x
be the mean of an SRS of size n from a population having mean μ and standard
deviation σ.
The mean and standard deviation of
x
are:
μ
x
= μ
σ
x
=
σ/
n
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 length of service calls
(σ
x
=
σ/
n
)
σ
=
184.81 seconds
SRS of 20 calls:
σ
x
=
SRS of 80 calls:
σ
x
=
•averaging over more calls reduces variability makes it more likely that
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 Fall '08
 ABDUS,S.
 Central Limit Theorem, Normal Distribution, Standard Deviation, Variance, Probability theory

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