document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150680>Question 1150680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The annual rate of return on investment in “Apple Company Fund” is normally distributed with mean of 20% and a standard deviation of 40%.<BR>\n" );
document.write( "(i) What is the probability that the annual rate of return on investment in “Apple Company Fund” is between 5% and 50%?<BR>\n" );
document.write( "(ii) Determine the annual rate of return such that the probability of exceeding it is 0.05. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772245 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=772245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i get the following.\r<BR>\n" );
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document.write( "mean is 20% and standard deviation is 40%.\r<BR>\n" );
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document.write( "probability the rate of return is between 5% and 50% is equal to .4195.\r<BR>\n" );
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document.write( "annual rate of return such that the probability of exceeding it is .05 would be 85.794%.\r<BR>\n" );
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document.write( "here are the visuals.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/122401.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/122402.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "if you don't have such a calculator as the one i used (found at http://davidmlane.com/hyperstat/z_table.html), then you might have to work with z-scores as shown below.\r<BR>\n" );
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document.write( "i)\r<BR>\n" );
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document.write( "z-score for annual rate of return of .05 is z = (5 - 20 / 40 = -.375.\r<BR>\n" );
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document.write( "z-score for annual rate of return of .5 is z = (50 - 20) / 40 = .75\r<BR>\n" );
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document.write( "area under the normal distribution curve to the left of z = -.375 = .35383.\r<BR>\n" );
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document.write( "area under the normal distribution curve to the left of z = .75 = .77337\r<BR>\n" );
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document.write( "area in between = .77337 - .35383 = .4195 rounded to 4 decimal places.\r<BR>\n" );
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document.write( "z-score that has area to the right of it of .05 is the same as z-score that has area of .95 to the left of it.\r<BR>\n" );
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document.write( "z-score with area of .95 to the left of it is equal to 1.64485.\r<BR>\n" );
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document.write( "raw score associated with that z-score is 1.64485 = (x - 20) / 40.\r<BR>\n" );
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document.write( "solve for x to get x = 1.64485 * 40 + 20 = 85.794.\r<BR>\n" );
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document.write( "i worked with percents, but you could also work with rates.\r<BR>\n" );
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document.write( "rate = percent / 100<BR>\n" );
document.write( "percent = rate * 100\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 mean<BR>\n" );
document.write( "s is the standard deviation or the standard error.<BR>\n" );
document.write( "in this case, standard deviation is used.<BR>\n" );
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