document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124867>Question 124867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 60. In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that few will need repair at manufacturer expense. On the other hand, the warranty period must be long enough to make the purchase attractive to the buyer. For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer’s expense? the answer is 32.56, I just need to know how this was computed by showing the work. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #91512 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a new HDTV the mean number of months until repairs are needed is 36.84 with a standard deviation of 3.34 months. Where should the warranty limits be set so that only 10 percent of the HDTVs need repairs at the manufacturer’s expense? the answer is 32.56, I just need to know how this was computed by showing the work.<BR>\n" );
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document.write( "Draw a normal curve; put the mean of 36.84 at the middle; mark some <BR>\n" );
document.write( "point on the horizontal axis as the point below which 10% of the population<BR>\n" );
document.write( "lies.<BR>\n" );
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document.write( "Find the corresponding z-value for that point: it is z=-1.2816<BR>\n" );
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document.write( "Find the corresponding \"x\" or raw-score value:<BR>\n" );
document.write( "z(x) = (x-mu)/sigma<BR>\n" );
document.write( "-1.281552 = (x-36.84)/3.34<BR>\n" );
document.write( "x-36 = 3.34*(-1.281552)<BR>\n" );
document.write( "x = 31.72 months<BR>\n" );
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document.write( "Comment It doesn't turn out to be 32.56 but it is correct if you are<BR>\n" );
document.write( "using a z-distribution<BR>\n" );
document.write( "But if you are supposed to use a t-distribution you would get:<BR>\n" );
document.write( "t(x) = (x-36.84)/3.34<BR>\n" );
document.write( "Using t = -1.282 you get:<BR>\n" );
document.write( "x-36 = -1.282*3.34 <BR>\n" );
document.write( "x = 31.72 months<BR>\n" );
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document.write( "Both results are the same.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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