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STAT 400
Examples for 10/27/2011
(1)
Fall 2011
1.
Suppose the lifetime of a particular brand of light bulbs is normally distributed with
standard deviation of
σ
= 75 hours and unknown mean.
a)
What is the probability that in a random sample of
n
= 49 bulbs, the average lifetime
X
is within 21 hours of the overall average lifetime?
b)
Suppose the sample average lifetime of
n
= 49 bulbs is
x
= 843 hours.
Construct a
95% confidence interval for the overall average lifetime for light bulbs of this brand.
A
confidence interval
is a
range of numbers
believed to include an unknown
population parameter.
Associated with the interval is a measure of the
confidence
we have that the interval does indeed contain the parameter of interest.
A
(1

α
) 100%
confidence
interval
for
the
population
mean
μ
when
σ
is known
and sampling is done from a normal
population, or with a large sample, is
⋅
α
+
⋅
α

σ
σ
n
z
n
z
,
2
2
X
X
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±
n
z
σ
⋅
α
2
X
±
ε
estimate
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