document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085112>Question 1085112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Clients enter a tax&#8203; preparer's office at an average rate of 8 per hour.  They enter randomly and independently of one another.<BR>\n" );
document.write( "Express your answers to four decimal places.  Express the probabilities as decimal fractions&#8203; -- not as percentages.<BR>\n" );
document.write( "a.  What is the probability that exactly 7 clients will enter the office in the next half&#8203; hour? <BR>\n" );
document.write( "nothing<BR>\n" );
document.write( "b.  What is the probability that at least one client enters the office in the next half&#8203; hour? <BR>\n" );
document.write( "nothing<BR>\n" );
document.write( "c.  What is the mean of the number of clients who will enter the office in the next half&#8203; hour? <BR>\n" );
document.write( "nothing<BR>\n" );
document.write( "d.  What is the variance of the number of clients who will enter the office in the next half&#8203; hour? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699280 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=699280\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This would be a Poisson distribution with mean 4 for a half hour<BR>\n" );
document.write( "Therefore,<BR>\n" );
document.write( "c=4 people<BR>\n" );
document.write( "d=4 people^2, since Poisson has mean=variance.<BR>\n" );
document.write( "Probability of 7 is e^(-4)*4^7/7!=0.0595<BR>\n" );
document.write( "probability of 0 clients is e^(-4)=0.0183<BR>\n" );
document.write( "1-0.0183=0.9817; this is the probability of at least 1 client. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );