document.write( "Question 1019893: The lengths of nails produced in a factory are normally distributed with a mean of
\n" ); document.write( "4.95 centimeters and a standard deviation of
\n" ); document.write( "0.05 centimeters. Find the two lengths that separate the top
\n" ); document.write( "5% and the bottom
\n" ); document.write( "5%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
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Algebra.Com's Answer #635823 by mathmate(429) $\"\"$ $\"About$

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\n" ); document.write( "Question:
\n" ); document.write( "The lengths of nails produced in a factory are normally distributed with a mean of
\n" ); document.write( "4.95 centimeters and a standard deviation of
\n" ); document.write( "0.05 centimeters. Find the two lengths that separate the top
\n" ); document.write( "5% and the bottom
\n" ); document.write( "5%. These lengths could serve as limits used to identify which nails should be rejected. Round your answer to the nearest hundredth, if necessary.
\n" ); document.write( "
\n" ); document.write( "Solution:
\n" ); document.write( "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.
\n" ); document.write( "
\n" ); document.write( "From normal distribution tables, the 95% and 5% cutoffs are Z=±1.65.
\n" ); document.write( "Since Z=(X-μ)/σ, we solve for X in terms of Z
\n" ); document.write( "X=±1.65σ+μ
\n" ); document.write( "=5.95±1.65*0.05=(4.868,5.032)
\n" ); document.write( "are the limits to the 5-95% bracket of lengths. \n" ); document.write( "

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