document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203397>Question 1203397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question 2\r<BR>\n" );
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document.write( "A.The table below shows the probability distribution for a discrete random variable X.\r<BR>\n" );
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document.write( "X	0	1	2	4	5<BR>\n" );
document.write( "P(X=x)	0.15	0.20	n	0.30	0.10<BR>\n" );
document.write( "Table 2.<BR>\n" );
document.write( "i.State the value of n	(1 mark)<BR>\n" );
document.write( "ii.Calculate the expectation value, E(X)	(4 marks)<BR>\n" );
document.write( "iii.Calculate the variance, Var(X)	(5 marks)\r<BR>\n" );
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document.write( "B.A random variable X follows a Normal probability distribution and has a mean value of 25 and a variance of 9. Calculate:<BR>\n" );
document.write( "i.P(X < 21)	(3 marks)<BR>\n" );
document.write( "ii.P(X > 26)	(3 marks)<BR>\n" );
document.write( "iii.P( 23 < X < 28)	(4 marks)<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 #839094 by </B><A HREF=/tutors/aboutme.mpl?userid=mntnvisions><B>mntnvisions(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mntnvisions><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=839094\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The total probability must be 1.0\r<BR>\n" );
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document.write( "Add the probabilities and solve for n.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1=+0.15+%2B0.20+%2Bn+%2B0.30%2B+0.10 ALIGN=MIDDLE  ALT=\"P=1=+0.15+%2B0.20+%2Bn+%2B0.30%2B+0.10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1-0.75=0.25 ALIGN=MIDDLE  ALT=\"n=1-0.75=0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "n=0.25\r<BR>\n" );
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document.write( "Mean or average value, use n=0.25 value.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E%28x%29=sum+%28xP%28x%29%29=0%2A0.15%2B++1%2A0.2%2B++2%2A0.25%2B++4%2A0.3%2B++5%2A0.1+=2.4 ALIGN=MIDDLE  ALT=\"E%28x%29=sum+%28xP%28x%29%29=0%2A0.15%2B++1%2A0.2%2B++2%2A0.25%2B++4%2A0.3%2B++5%2A0.1+=2.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Variance.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Var%28x%29=sum%28%28x-E%28x%29%29%5E2%29P%28x%29=0.15%28-2.4%29%5E2%2B0.2%28-1.4%29%5E2%2B0.25%28-.4%29%5E2%2B0.3%281.6%29%5E2%2B0.1%282.6%29%5E2+=2.74 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "B.A random variable X follows a Normal probability distribution and has a mean value of m=25 and a variance of Var=9. Calculate:\r<BR>\n" );
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document.write( "Standard deviation = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s=sqrt%28Var%29=sqrt%289%29=3 ALIGN=MIDDLE  ALT=\"+s=sqrt%28Var%29=sqrt%289%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "i.P(X < 21):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28X-m%29%2Fs=%2821-25%29%2F3=-4%2F3 ALIGN=MIDDLE  ALT=\"z=%28X-m%29%2Fs=%2821-25%29%2F3=-4%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Z+%3C+-1.333%29=0.0912 ALIGN=MIDDLE  ALT=\"P%28Z+%3C+-1.333%29=0.0912\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "ii.P(X > 26) \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28X-m%29%2Fs=%2826-25%29%2F3=1%2F3 ALIGN=MIDDLE  ALT=\"z=%28X-m%29%2Fs=%2826-25%29%2F3=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28Z+%3E+0.333%29=1-P%28Z+%3C+0.333%29=1-0.631=0.369 ALIGN=MIDDLE  ALT=\"P%28Z+%3E+0.333%29=1-P%28Z+%3C+0.333%29=1-0.631=0.369\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "iii.P( 23 < X < 28):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%28X-m%29%2Fs=%2823-25%29%2F3=-2%2F3 ALIGN=MIDDLE  ALT=\"a=%28X-m%29%2Fs=%2823-25%29%2F3=-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%2828-25%29%2F3=1 ALIGN=MIDDLE  ALT=\"b=%2828-25%29%2F3=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28-0.667+%3CZ+%3C+1%29=P%28Z+%3C+1%29-P%28Z+%3C+-0.667%29=0.841-0.252=0.589 ALIGN=MIDDLE  ALT=\"P%28-0.667+%3CZ+%3C+1%29=P%28Z+%3C+1%29-P%28Z+%3C+-0.667%29=0.841-0.252=0.589\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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