document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203818>Question 1203818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A distribution of values is normal with a mean of 144 and a standard deviation of 73.2.\r<BR>\n" );
document.write( "\n" );
document.write( "Find P4, which is the score separating the bottom 4% from the top 96%. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839657 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=839657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 144.<BR>\n" );
document.write( "standard deviation is 73.2<BR>\n" );
document.write( "P4 is the score that separates the bottom 4% from the top 96%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use a normal distribution calculator to find the z-score that has 4% of the area under the normal distribution curv to the left of it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "one such calcuator 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>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this calculator tells you that the the z-score with an area to the left of it of .04 is equal to -1.751.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "use the z-score formula to find the associated raw score.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the z-score formula is z = (x - m) / s<BR>\n" );
document.write( "x is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula becomes -1.751 = (x - 144) / 73.2<BR>\n" );
document.write( "solve for to get:<BR>\n" );
document.write( "z = -1.751 * 73.2 + 144 = 15.8268.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P4 is equal to 15.8268.<BR>\n" );
document.write( "that's the score that separates the bottom 4% from the top 96% of the scores when the mean is 144 and the standard deviation is 73.2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's what the calculator results look like.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092201.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );