document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134479>Question 1134479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A study of the impact of executive networking on firm performance measured firm performance as annual return on equity​ (ROE), recorded as a percentage. The mean ROE for the firms studied was 14.93​% and the standard deviation was 21.74​%. Assume that these values represent mu and sigma for the population ROE distribution and that this distribution is normal. What value of ROE will be exceeded by 78​% of the​ firms?<BR>\n" );
document.write( "The value of ROE that will be exceeded by 78​% of the firms is blank %.<BR>\n" );
document.write( "​(Round to two decimal places as​ needed.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751866 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=751866\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is 14.93%<BR>\n" );
document.write( "the standard deviation is 21.74%\r<BR>\n" );
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document.write( "you want to know what value of ROE will be exceeded by 78% of the firms.\r<BR>\n" );
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document.write( "in a normal distributuion, 78% of the area under the nomral distribution curve to the right of the z-score would generate a z-score equal to -.7721932195.\r<BR>\n" );
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document.write( "the z-score formula is z = (x - m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw score mean<BR>\n" );
document.write( "s is the standard deviation\r<BR>\n" );
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document.write( "this formula becomes -.7721932195 = (x - 14.93) / 21.74.\r<BR>\n" );
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document.write( "solve for x to get x = 21.74 * -.7721932195 + 14.93 =  -1.857480591 percent.\r<BR>\n" );
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document.write( "this can be seen visually in the following graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/020906.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "78% of the firms will provide a ROE greater than -1.857480591 percent.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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