document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200611>Question 1200611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the scores of students on an exam are Normally distributed with a mean of 488 and a standard deviation of 67. Then approximately 99.7% of the exam scores lie between the numbers <BR>\n" );
document.write( " and <BR>\n" );
document.write( " such that the mean is halfway between these two integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834784 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=834784\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean is 488 and standard deviation is 67.<BR>\n" );
document.write( "99.7% of the exam scores lie between 289.162 and 686.838<BR>\n" );
document.write( "critical z-score for two tailed confidence interval os .997 is equal to plus or minus 1.967737927.<BR>\n" );
document.write( "low z-score formula becomes -2.967737927 = (x - 488) / 67.<BR>\n" );
document.write( "solve for x to get x = 67 * -2.967737927 + 488 = 289.163<BR>\n" );
document.write( "high z-score formula becomes 2.967737927 = (x - 488) / 67.<BR>\n" );
document.write( "solve for x to get x = 67 * 2.967737927 + 488 = 686.838.<BR>\n" );
document.write( "i did it the easy way by using the calculator 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( "here are the results from using that calculator.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/022702.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );