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The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resistance exceedin
Question
The distribution of resistance for resistors of a certain type is known to be normal, with 10% of all resistors having a resistance exceeding 10.256 ohms and 5% having a resistance smaller than 9.671 ohms. What are the mean value and standard deviation of the resistance distribution? slader
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Physics
3 years
2021-08-24T23:22:41+00:00
2021-08-24T23:22:41+00:00 1 Answers
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Answers ( )
Explanation:
Formula for the given probability is as follows.
According to the normal table area we have,
P(z < 1.28) = 0.10
Hence,![Rendered by QuickLaTeX.com \frac{10.256 - \mu}{\sigma} = 1.28](https://documen.tv/wp-content/ql-cache/quicklatex.com-ae3612525f78dbd7f2ea5f29ed9e82c4_l3.png)
Also, the given probability is as follows.
Hence,![Rendered by QuickLaTeX.com \frac{9.671 - \mu}{\sigma} = -1.645](https://documen.tv/wp-content/ql-cache/quicklatex.com-5eff6a20c86d6156878cfeec529730c2_l3.png)
Now, substitute the value of
from equation (1) into equation (2) as follows.
Putting the value of
into equation (2) we will find the value of
as follows.
=
= 10
Thus, we can conclude that the value of
is 0.2 and the value of
is 10.