document.write( "Question 506226: A manufacturer found that among 500 randomly selected smoke detectors only 450 worked properly. Based on this information, how many smoke detectors would you have to install to be sure that the probability that at least one of them will work will be at least 99.99% \n" ); document.write( "

Algebra.Com's Answer #340113 by stanbon(75887) $\"\"$ $\"About$

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A manufacturer found that among 500 randomly selected smoke detectors only 450 worked properly. Based on this information, how many smoke detectors would you have to install to be sure that the probability that at least one of them will work will be at least 99.99%
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\n" ); document.write( "Binomial Problem with n unknown and p = 450/500 = 0.9
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\n" ); document.write( "Solve P(1<= x <=n)> = 0.9999
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\n" ); document.write( "P(1<= x <=n) = 1 - P(x = 0) = 1 - 0.1^n
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\n" ); document.write( "Solve: 1 - 0.1^n >= 0.9999
\n" ); document.write( "0.1^n <= 0.0001
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\n" ); document.write( "Take the log:
\n" ); document.write( "n*log(0.1) <= -4
\n" ); document.write( "n*(-1)<= -4
\n" ); document.write( "n >= 4
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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