document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333728>Question 333728</A>: <I><SPAN STYLE=\"word-break: break-all;\">   According to Investment Digest (\"Diversification and the Risk/Reward Relationship\", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 15.4%, and the standard deviation of the annual return was 24.5%.  During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 6.0%.  The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric.  Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously. \r<BR>\n" );
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document.write( "Find the probability that the return for common stocks will be greater than 9%. <BR>\n" );
document.write( "Find the probability that the return for common stocks will be greater than 25%. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #239175 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=239175\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> According to Investment Digest (\"Diversification and the Risk/Reward Relationship\", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 15.4%, and the standard deviation of the annual return was 24.5%. During the same 67-year time span, the mean of the annual return for long-term government bonds was 5.5%, and the standard deviation was 6.0%. The article claims that the distributions of annual returns for both common stocks and long-term government bonds are bell-shaped and approximately symmetric. Assume that these distributions are distributed as normal random variables with the means and standard deviations given previously.<BR>\n" );
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document.write( "Find the probability that the return for common stocks will be greater than 9%.<BR>\n" );
document.write( "z(0.09) = (0.09-0.154)/0.245 = -0.2612<BR>\n" );
document.write( "P(x > 0.09) = P(z> -0.2612) = 0.6930<BR>\n" );
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document.write( "Find the probability that the return for common stocks will be greater than 25%.<BR>\n" );
document.write( "z(25) = (25-15.4)/24.5 = 0.3918<BR>\n" );
document.write( "P(x > 25%) = P(z > 0.3918) = 0.3476<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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