document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1145394>Question 1145394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Oasis is an asset management company in South Africa. It has found that there is a three-in-five chance that a general equity unit trust fund will perform better than the overall JSE share index over any one-year period. If seven general equity unit trust funds are randomly selected from general equity unit trust funds.\r<BR>\n" );
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document.write( "2.1)	What is the probability that all of these general equity unit trust funds performed better than the overall JSE share index over the past year (rounded off to three decimals)?			  [2]<BR>\n" );
document.write( "2.2)	What is the probability that at most two of these general equity trust funds performed better than the overall JSE share index over the past year (rounded off to three decimals)?		            [3.5]<BR>\n" );
document.write( "2.3)	What is the probability that more than two but less than five performed worse than the overall JSE share index over the past year (rounded off to three decimals)?				            [3.5]<BR>\n" );
document.write( "2.4)	For 150 general equity unit trust funds, what is the expected number of general equity unit trust funds that will perform better than the overall JSE share index (rounded off to zero decimals)?	  [1]\r<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 #766616 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=766616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b>2.1) What is the probability that all of these general equity unit trust funds performed better than the overall JSE share index over the past year (rounded off to three decimals)?</b><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.6%29%5E7 ALIGN=MIDDLE  ALT=\"%280.6%29%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.028<BR>\n" );
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document.write( "<b>2.2) What is the probability that at most two of these general equity trust funds performed better than the overall JSE share index over the past year (rounded off to three decimals)?</b><BR>\n" );
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document.write( "Probability exactly two performed better: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.6%29%5E2%2A%280.4%29%5E5%2A%287%21%2F%282%21%2A5%21%29%29 ALIGN=MIDDLE  ALT=\"%280.6%29%5E2%2A%280.4%29%5E5%2A%287%21%2F%282%21%2A5%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.077<BR>\n" );
document.write( "Probability exactly one performed better: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.6%29%5E1%2A%280.4%29%5E6%2A%287%21%2F%281%21%2A6%21%29%29 ALIGN=MIDDLE  ALT=\"%280.6%29%5E1%2A%280.4%29%5E6%2A%287%21%2F%281%21%2A6%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.017<BR>\n" );
document.write( "Probability exactly none performed better: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.4%29%5E7 ALIGN=MIDDLE  ALT=\"%280.4%29%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.002<BR>\n" );
document.write( "Probability \"at most two\" performed better: 0.077 + 0.017 + 0.002 = 0.096<BR>\n" );
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document.write( "<b>2.3) What is the probability that more than two but less than five performed worse than the overall JSE share index over the past year (rounded off to three decimals)?</b><BR>\n" );
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document.write( "The probability that \"more than two but less than five\" performed worse is another way of asking what the probability is that three or four performed worse.  (Also note is says performed \"worse\", not \"better\".)<BR>\n" );
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document.write( "Probability exactly three performed worse: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.4%29%5E3%2A%280.6%29%5E4%2A%287%21%2F%283%21%2A4%21%29%29 ALIGN=MIDDLE  ALT=\"%280.4%29%5E3%2A%280.6%29%5E4%2A%287%21%2F%283%21%2A4%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.290<BR>\n" );
document.write( "Probability exactly four performed worse: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.4%29%5E4%2A%280.6%29%5E3%2A%287%21%2F%284%21%2A3%21%29%29 ALIGN=MIDDLE  ALT=\"%280.4%29%5E4%2A%280.6%29%5E3%2A%287%21%2F%284%21%2A3%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.194<BR>\n" );
document.write( "Probability \"more than two but less than five\" performed worse: 0.290 + 0.194 = 0.484<BR>\n" );
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document.write( "<b> For 150 general equity unit trust funds, what is the expected number of general equity unit trust funds that will perform better than the overall JSE share index (rounded off to zero decimals)?</b><BR>\n" );
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document.write( "150 * 0.60 = 90 </SPAN>\n" );
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