document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1167865>Question 1167865</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a life insurance company  sells a $190,000 one year term life insurance policy to a 25- year old female for $370. The probability that the female survives the year is 0.999536. Compute and interpret the expected value of this policy to the insurance company.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #792479 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=792479\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the woman does not survive the year, the company pays out 190,000 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the woman survives the year, the company keeps the 370 dollars and pay out nothing.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability that the woman survives the year is .999536.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability that the woman doesn't survive the year is 1 minus that = .000464.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the expected value is 370 - .000464 * 190,000 = 281.84 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the company gets 370 from everybody who buys that same policy and the company pays out 190,000 for anybody who does not survive the year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is how it works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "suppose the company sold the same policy to 1 million 25 year old females.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the company collects 1 million * 370 = 370 million dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".000464 * 100 = .0464% of the females die within the year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be .000464 * 1 million = 464 females who bought the policy that do not survive the year.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the company pays out 464 * 190,000 = 88.160 million dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the company net revenue for the year = 370 million minus 88.160 million = 281.84 million.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide that by 1 million customers and you get average net revenue of 281.84 per customer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that's the expected value for each customer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );