document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469817>Question 469817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> All the major stock market indexes posted heavy losses in 2008. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was -38.5%. The mean one year return for the NASDAQ, a group of 3,200 small and medium sized companies, was -40.5%. Historically, the one year return are approximately normal, the standard deviation in the S&P 500 is approximately 20%, and the standard deviation in the NASDAQ is approximately 30%.	  a. What is the probability that a stock in the S&P 500 gained value in 2008?	 b. What is the probability that a stock in the S&P 500 gained 10% more?	 c. What is the probability that a stock in the S&P 500 lost 50% more in 2008?	 d. What is the probability that a stock in the S&P 500 lost 60% more?	 e. Repeat (a) through (d) for a stock in the NASDAQ.	 f. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322303 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=322303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> All the major stock market indexes posted heavy losses in 2008. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was -38.5%. The std = 20%<BR>\n" );
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document.write( "The mean one year return for the NASDAQ, a group of 3,200 small and medium sized companies, was -40.5%. The std is 30%<BR>\n" );
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document.write( "a. What is the probability that a stock in the S&P 500 gained value in 2008? <BR>\n" );
document.write( "z(0) = (0-(-38.5))/20 = 1.925<BR>\n" );
document.write( "P(x > 0) = P(z > 1.925 = 0.0271<BR>\n" );
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document.write( "b. What is the probability that a stock in the S&P 500 gained 10% more? <BR>\n" );
document.write( "Find the z-value of 10<BR>\n" );
document.write( "Find the probability of z being >= that z-value<BR>\n" );
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document.write( "c. What is the probability that a stock in the S&P 500 lost 50% more in 2008?<BR>\n" );
document.write( "Find the z-value of -50<BR>\n" );
document.write( "Find the probability of z being <= that z-value<BR>\n" );
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document.write( "d. What is the probability that a stock in the S&P 500 lost 60% more? <BR>\n" );
document.write( "? more than what?\r<BR>\n" );
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document.write( "e. Repeat (a) through (d) for a stock in the NASDAQ. f. Write a short summary on your findings. Be sure to include a discussion of the risks associated with a large standard deviation.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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