document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164283>Question 1164283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The human resources division in a large government department has shown that illness is given<BR>\n" );
document.write( "as the reason for absenteeism from work in 80% of absenteeism cases. Suppose a group of 100<BR>\n" );
document.write( "employees who had been absent are randomly selected. Find the approximate probability that<BR>\n" );
document.write( "at most 86 of them gave illness as their reason for absence. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788636 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788636\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use normal approximation<BR>\n" );
document.write( "mean is np=100*0.80=80<BR>\n" );
document.write( "variance is np(1-p)=80*0.2=16<BR>\n" );
document.write( "sd is sqrt(16)=4<BR>\n" );
document.write( "the approximate probability would be z<=(x+0.5-mean)/sd=(86.5-80)/4=1.625. The +0.5 is the continuity correction factor.<BR>\n" );
document.write( "that probability is 0.9479\r<BR>\n" );
document.write( "\n" );
document.write( "The exact probability is 0.9531. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );