document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=317453>Question 317453</A>: <I><SPAN STYLE=\"word-break: break-all;\">    Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent.  Considering drawing a sample of n = 5 stocks.  Find the mean and the standard deviation of the sampling distribution of X, and find an interval containing 95.44 percent of all possible sample mean returns.\r<BR>\n" );
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document.write( "    I don't have any work to show because I have no idea where to start. I would appreciate any assistance you can give me.  Thanking you in advance for your time and effort.  Have a beautiful day.\r<BR>\n" );
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document.write( "    Natasha j   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #284024 by </B><A HREF=/tutors/aboutme.mpl?userid=butterflyinschool><B>butterflyinschool(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=butterflyinschool><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=284024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that the percentage returns for a given year for all stocks listed on the New York Stock Exchange are approximately normally distributed with a mean of 12.4 percent and a standard deviation of 20.6 percent. <BR>\n" );
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document.write( "Considering drawing a sample of n = 5 stocks. Find the mean and the standard deviation of the sampling distribution of X, <BR>\n" );
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document.write( "The mean of the sample means of size n=5 = 12.4%<BR>\n" );
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document.write( "The standard deviation of the sample means of size 5 = 20.6%/sqrt(5) = 0.0921<BR>\n" );
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document.write( "Note: To understand this read what your text says about \"The Central <BR>\n" );
document.write( "Limit Theorem\".<BR>\n" );
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document.write( "Find an interval containing 95.44 percent of all possible sample mean returns.<BR>\n" );
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document.write( "Draw the picture of 95.44% centered on the mean. That puts 0.4772 to the<BR>\n" );
document.write( "left of the middle, leaving a left-most tail of 0.0228.<BR>\n" );
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document.write( "Find the z-value with a left tail of 0.0228<BR>\n" );
document.write( "InvNorm(0.0228) = z = -1.999<BR>\n" );
document.write( "Correspondingly, there is an upper bound of z = +1.999<BR>\n" );
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document.write( "Find the corresponding x-values<BR>\n" );
document.write( "x = zs + u<BR>\n" );
document.write( "x = -1.999*0.0921 + 0.124 = -1.78%<BR>\n" );
document.write( "x = 1.999*0.0921 + 0.124 = 30.81%<BR>\n" );
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