Recap for Confidence Interval for the Mean (σ
Known)
A confidence interval is a range of values that has a
prespecified probability of including the true value of
the parameter.
Therefore, a confidence interval for
the mean is a range of values that has a prespecified
probability of including the mean, µ.
The formula for a
confidence interval for the mean when σ is known is:
x
±
z
α
/2
σ
/
√
n .
The value of
α/2
z
(sometimes written as just “z”)
depends on the level of confidence.
The higher the
level of confidence, the larger the zscore.
For
example, an 80% confidence interval for the mean is:
x
1.28
n
σ
±
, whereas a 95% confidence interval for
µ is:
x
1.96
n
σ
±
.
You should know how to
determine the value of
α/2
z
for the desired confidence
level.
150
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Example
:
Genron Corp. would like to determine the
mean length of life for the highperformance model of
tires that it supplies to an American automobile
manufacturer.
Forty tires are randomly selected from
the manufacturing process and subjected to
accelerated lifetesting.
The mean from the sample is
33,127 miles.
Assume that the standard deviation for
the population of tires (that is, σ) is 7,500 miles.
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 Fall '09
 Rollins
 Normal Distribution, Student's tdistribution

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