STAT 409
Examples for 09/14/2009
Fall 2009
1.
Suppose the lifetime of a particular brand of light bulbs is normally distributed with
standard deviation of 75 hours and unknown mean.
a)
What is the probability that in a random sample of 49 bulbs, the average lifetime
X
is within 21 hours of the overall average lifetime?
σ
= 75,
n
= 49.
P(
μ
– 21 <
X <
μ
+ 21
) =
(
29
(
29

+
<
<


49
75
21
Z
49
75
21
P
μ
μ
μ
μ
= P(
–
1.96 < Z < 1.96
) =
0.95
.
b)
Suppose the sample average lifetime of the 49 bulbs is
x
= 843 hours.
Construct a
95% confidence interval for the overall average lifetime for light bulbs of this brand.
(
X – 21,
X + 21
)
(
822
,
864
)
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
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 Spring '11
 Stepanov
 Normal Distribution, Probability, Standard Deviation, σ, α, overall average lifetime

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