document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205164>Question 1205164</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows the mean is 8.4 hours and the standard deviation is 1.8 hours. Find the probability that a randomly selected mechanic has a rebuild time more than 8 hours. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841808 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=841808\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 8.4 hours<BR>\n" );
document.write( "standard deviation is 1.8 hours.<BR>\n" );
document.write( "probability of randomly selected mechanic has a rebuild time greater than 8 hours?<BR>\n" );
document.write( "use the z-score.<BR>\n" );
document.write( "z = (x-m)/s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the random mechanic time.<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation.<BR>\n" );
document.write( "formula becomes z = (8 - 8.4) / 1.8 = -.2222<BR>\n" );
document.write( "area to the right of that z-score is equal to .5879.<BR>\n" );
document.write( "that's the probability that the randomly selected mechanic will take more than 8 hours to rebuild the transmission.<BR>\n" );
document.write( "here's what it looks like on a graph using z-scores.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/112902.jpg\">\r<BR>\n" );
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document.write( "here's what it looks like on a graph using raw scores.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/112901.jpg\">\r<BR>\n" );
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document.write( "when using z-scores, the mean is 0 and the standard deviation is 1.\r<BR>\n" );
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document.write( "when using raw scores, the mean is what it is and the standard deviation is what it is .\r<BR>\n" );
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document.write( "the calculator that generated that graph can be found at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );