document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1139689>Question 1139689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the percentage of bulbs that can be expected to last the period of time. Round to the nearest hundredth, if necessary.\r<BR>\n" );
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document.write( "Less than 520 hours<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760193 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=760193\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 500 hours.<BR>\n" );
document.write( "standard deviation is 100 hours.<BR>\n" );
document.write( "number of light bulbs installed is 5000.\r<BR>\n" );
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document.write( "z = (x - m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw mean<BR>\n" );
document.write( "s is the standard error, which, in this case, is the standard deviation, since you are dealing with the population of 5000 light bulbs rather than a sample of a much larger population.\r<BR>\n" );
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document.write( "in this problem, the formula becomes z = (520 - 500) / 100.\r<BR>\n" );
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document.write( "solve for z to get z = 20 / 100 = .2\r<BR>\n" );
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document.write( "with a z-score of .2, the percentage of bulbs that can be expected to last less than 520 hours would be equal to .5792596878 * 100 = 57.92596878%.\r<BR>\n" );
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document.write( "round to 2 decimal places and the solution is 57.93%\r<BR>\n" );
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