Question 1019893: The lengths of nails produced in a factory are normally distributed with a mean of
4.95 centimeters and a standard deviation of
0.05 centimeters. Find the two lengths that separate the top
5% and the bottom
5%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website!
Question:
The lengths of nails produced in a factory are normally distributed with a mean of
4.95 centimeters and a standard deviation of
0.05 centimeters. Find the two lengths that separate the top
5% and the bottom
5%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
Solution:
The top and bottom 5% can be obtained as a multiple of the standard deviation (σ) using the normal distribution curve, and the definition of Z=(X-μ)/σ.
From normal distribution tables, the 95% and 5% cutoffs are Z=±1.65.
Since Z=(X-μ)/σ, we solve for X in terms of Z
X=±1.65σ+μ
=5.95±1.65*0.05=(4.868,5.032)
are the limits to the 5-95% bracket of lengths.
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