document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180015>Question 1180015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose 200 people are lined up side-by-side, each one holding a fair coin. Each person flips their coin 64 times; every time it lands heads they step 1 meter forward, each time it lands tails they step 1 meter backward. Use a normal approximation to answer the following question: after everyone finishes their 64 steps, approximately how many people will be standing between 4 and 8 meters behind the starting line? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850151 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</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=850151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I agree with the solution by @CPhill almost everywhere, except of its final part.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "After the number of interest of heads is determined to be  between 28 and 30 inclusive,\r<BR>\n" );
document.write( "\n" );
document.write( "the continuity correction should be applied.\r<BR>\n" );
document.write( "\n" );
document.write( "Thus, actually, we look for the probability for H to be between 27.5 and 30.5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, in the solution by @CPhill the z-scores z1 and z2 should be modified consistently.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The final answer for the probability is then 0.2235 instead of 0.1498,<BR>\n" );
document.write( "and the number of people between -8 and -4 meters is then about 0.2235*200 = 44.7,<BR>\n" );
document.write( "or about 45.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This difference is significant and, therefore, should be accounted.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );