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boneill3
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Homework Statement
A standard light bulb is claimed to have a lifelength of 8000 hours with standard deviation of 800 hours.
A newly designed light bulb is claimed to have a life length of 9200 hours with a standard deviation of 600 hours
Homework Equations
If 36 standard and 36 newly designed bulbs are tested what is the probability that the mean lifelength of the standard bulbs will be greater than the mean lifelength of the newly designed bulbs.
[itex]
z = \frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}
[/itex]
The Attempt at a Solution
Since the sample size is greater than 30, the central limit theorem can be used
[itex]
z = \frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}
[/itex]
We have [itex]\sigma [/itex] = 600
n = 36
[itex]\mu [/itex]= 9200 ( the mean of the newly designed bulbs.)
X = 8000 ( the mean of the standard bulbs.)
Putting those into the formula we get:
[itex]
z = \frac{8000-9200}{\frac{\600}{\sqrt{36}}}
[/itex]
[itex]
z = \frac{8000-9200}{\frac{400}{3}}
[/itex]
= -1
which -1 standard deviations from mean so equates to aprroximately .85 on the normal distribution.
So the probability that the mean lifelength of the standard bulbs will be greater than the mean lifelength of the newly designed bulbs.
equals 1-0.85 = .15
How does that look ?