document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081996>Question 1081996</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Please help me solve the following probability question\r<BR>\n" );
document.write( "\n" );
document.write( "The average length of stay in a hospital is useful for planning purposes. Suppose that the following is the distribution of the length of stay in a hospital after a minor operation.\r<BR>\n" );
document.write( "\n" );
document.write( "   x =  1,   2,   3,    4,    5<BR>\n" );
document.write( "P(x) =  0.6, 0.1, 0.04, 0.02, c\r<BR>\n" );
document.write( "\n" );
document.write( "What is the average length of stay in the hospital? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696039 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=696039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given Distribution<BR>\n" );
document.write( "<TABLE  border=1>\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD></tr><tr><TD >P(X)</TD><TD >0.6</TD><TD >0.1</TD><TD >0.04</TD><TD >0.02</TD><TD >c</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First we need to know the value of c. The probabilities must add to 1 for this to be a true probability distribution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.6+0.1+0.04+0.02+c = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.76+c = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0.76+c-0.76 = 1-0.76\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "c = 0.24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the probability distribution updates to<BR>\n" );
document.write( "<TABLE  border=1>\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD></tr><tr><TD >P(X)</TD><TD >0.6</TD><TD >0.1</TD><TD >0.04</TD><TD >0.02</TD><TD >0.24</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To find the average, multiply the probabilities with their corresponding x values. Then add up those products.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1*0.6+2*0.1+3*0.04+4*0.02+5*0.24 = 2.2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------------------------------------<BR>\n" );
document.write( "----------------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Final Answer: The average length of stay in the hospital is <font color=red>2.2 days</font>\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );