document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187839>Question 1187839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Paul and Carlos began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Paul took a test in Science and earned a 79.7, and Carlos took a test in Art History and earned a 67.7. Use the fact that all the students' test grades in the Science class had a mean of 72.1 and a standard deviation of 10.5, and all the students' test grades in Art History had a mean of 61.9 and a standard deviation of 10.3 to answer the following questions.\r<BR>\n" );
document.write( "\n" );
document.write( "a) Calculate the z-score for Paul's test grade.<BR>\n" );
document.write( "z = <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "b) Calculate the z-score for Carlos's test grade.<BR>\n" );
document.write( "z =<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818864 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52814)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818864\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Paul and Carlos began arguing about who did better on their tests, but they couldn't decide who did better given that <BR>\n" );
document.write( "they took different tests. Paul took a test in Science and earned a 79.7, and Carlos took a test in Art History and earned a 67.7. <BR>\n" );
document.write( "Use the fact that all the students' test grades in the Science class had a mean of 72.1 and a standard deviation of 10.5, <BR>\n" );
document.write( "and all the students' test grades in Art History had a mean of 61.9 and a standard deviation of 10.3 to answer the following questions.\r<BR>\n" );
document.write( "\n" );
document.write( "a) Calculate the z-score for Paul's test grade.<BR>\n" );
document.write( "z = <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "b) Calculate the z-score for Carlos's test grade.<BR>\n" );
document.write( "z =<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "\r\n" );
document.write( "Use the formula for z-score\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Z = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+mu%29%2Fsigma ALIGN=MIDDLE  ALT=\"%28x+-+mu%29%2Fsigma\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Z	=	standard score\r\n" );
document.write( "x	=	observed value\r\n" );
document.write( "mu	=	mean of the sample\r\n" );
document.write( "sigma	=	standard deviation of the sample\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use this formula separately for each case.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then compare two resulting values of the z-scores.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "That's all.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );