document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193377>Question 1193377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1000 light bulbs with an average life of 120 days are<BR>\n" );
document.write( "installed in streets of Mumbai. Their length of life is normally<BR>\n" );
document.write( "distributed with variance 400 days. (i) How many will expire in<BR>\n" );
document.write( "less than 90 days? (ii) If it is decided to replace all the bulbs<BR>\n" );
document.write( "together what interval should be allowed between<BR>\n" );
document.write( "replacements if not more than 10% should expire before<BR>\n" );
document.write( "replacement?<BR>\n" );
document.write( "This question is related to normal distribution and standard normal variate<BR>\n" );
document.write( "My answer for(i) 668 but didn't get the answer for(ii) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825429 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 120 days<BR>\n" );
document.write( "variance is 400 days<BR>\n" );
document.write( "standard deviation is sqrt(400) = 20 days<BR>\n" );
document.write( "z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x if the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation\r<BR>\n" );
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document.write( "formula becomes:<BR>\n" );
document.write( "z = (90 - 120) / 20 = -1.5<BR>\n" );
document.write( "area under normal distribution curve less than z-score of -1.5 = .0668072287.<BR>\n" );
document.write( ".0668072287 * 1000 = 66.8072287\r<BR>\n" );
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document.write( "if you don't want more than 10% to expire before replacement, then the z-score for for an area of 10% to the left of it is equal to -1.281551567.<BR>\n" );
document.write( "use the z-score formula to find the raw score.<BR>\n" );
document.write( "-1.281551567 = (x - 120) / 20 = 94.36898867<BR>\n" );
document.write( "solve for x to get x = -1.281551567 * 20 + 120 = 94.36896867.<BR>\n" );
document.write( "is you don't want more than 10% to fail before replacing, then you should replace bulbs when no more than 94 days have elapsed before replacing.\r<BR>\n" );
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document.write( "my solutions to your questions are:\r<BR>\n" );
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document.write( "(i) How many will expire in<BR>\n" );
document.write( "less than 90 days? \r<BR>\n" );
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document.write( "66.8072287 are expected to expire in under 90 days.\r<BR>\n" );
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document.write( "(ii) If it is decided to replace all the bulbs together what interval should be allowed between replacements if not more than 10% should expire before replacement?\r<BR>\n" );
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document.write( "no more than 94.36896867 days should be allowed before replacing defective light bubs.\r<BR>\n" );
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document.write( "round as required.\r<BR>\n" );
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document.write( "let me know if you have any questions and whether or not these numbers were good for you.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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