document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1073724>Question 1073724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Life time of an automatic dishwasher is normally distributed with mean 3.5 years<BR>\n" );
document.write( "and<BR>\n" );
document.write( "S.D = 1.0 yrs. If a dishwasher is guaranteed for 12 months, what is the fraction of the sale that will require replacement? Mean 2,5 and SD 1.5 yrs guaranteed 6 months. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #688501 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=688501\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> calculator used can be found at this link:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">http://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "mean = 3.5 years = 42 months<BR>\n" );
document.write( "standard deviation = 1 year - 12 months<BR>\n" );
document.write( "guaranteed for 12 months.<BR>\n" );
document.write( "approximately .62% of the machines will fail within the first 12 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032101.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "mean = 2 years = 24 months<BR>\n" );
document.write( "standard deviation = 1.5 years = 18 months<BR>\n" );
document.write( "guaranteed for 6 months.<BR>\n" );
document.write( "approximately 15.87% of the machines will fail within the first 6 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this calculator allows you to use raw scores or z-scores.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z-score = (x-m)/s\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x is the raw score.<BR>\n" );
document.write( "m is the mean raw score.<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the first problem:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 12<BR>\n" );
document.write( "m = 42<BR>\n" );
document.write( "s = 12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = (12 - 42) / 12 = 30 / 12 = -2.5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "from the z-score tables, the area under the distribution curve to the left of a z-score of -2.5 will be .0062 = .62%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "same answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z-score table used can be found at:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<ahref= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\" target = \"_blank\">http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use of the lane normal distribution calculator will provide the same result as shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/032103.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );