document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164775>Question 1164775</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Approximately 20% of corporate workforce are not happy with their immediate<BR>\n" );
document.write( "bosses. Suppose 10 workers working in corporates are randomly selected.<BR>\n" );
document.write( "a) What is the probability that everybody of them is happy with his immediate<BR>\n" );
document.write( "boss?<BR>\n" );
document.write( "b) What is the probability that at least two of the workers are unhappy with<BR>\n" );
document.write( "their immediate bosses? <BR>\n" );
document.write( "c) What is the probability that no more than two of the workers are unhappy<BR>\n" );
document.write( "with their immediate bosses? <BR>\n" );
document.write( "d) Calculate the expected value and variance of the distribution </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789203 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=789203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .80 are happy so for all 10 to be happy is .80^10=0.1074<BR>\n" );
document.write( "at least 2 are unhappy.<BR>\n" );
document.write( "We know the probability that 0 are unhappy <BR>\n" );
document.write( "probability that 1 is unhappy is 10*0.2*0.8^9=0.2684<BR>\n" );
document.write( "so the probability that at least 2 are unhappy is 1-0.1074-0.2684=0.6242<BR>\n" );
document.write( "the probability that no more than 2 workers are unhappy is the probability 0 are+prob 1 is+prob 2 are.<BR>\n" );
document.write( "We know the first two.  The probability that 2 are is 10C2*0.2^2*0.8^8=0.3020<BR>\n" );
document.write( "The answer is 0.6778. Also on calculator with bincomcdf(10,0.2,2)ENTER\r<BR>\n" );
document.write( "\n" );
document.write( "expected value depends upon whether we are talking about happy (np=8) or unhappy (np=2) workers<BR>\n" );
document.write( "variance is the same for both (np(1-p))=1.6 workers  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );