document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=694369>Question 694369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find each probability\r<BR>\n" );
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document.write( "a. P(5;4)\r<BR>\n" );
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document.write( "b. P(2;4)\r<BR>\n" );
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document.write( "c. P(6;3)\r<BR>\n" );
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document.write( "d. P(10;7)\r<BR>\n" );
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document.write( "e. P(9;8)\r<BR>\n" );
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document.write( "Part 2\r<BR>\n" );
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document.write( "A copy machine randomly puts out 10 blank sheets per 500 copies processed. Find the probability that in a run of 300 copies, 5 sheets of paper will be blank.\r<BR>\n" );
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document.write( "Part 3\r<BR>\n" );
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document.write( "A recent study of robberies for a certain geographic region showed an average of 1 robbery per 20,000 people. In a city of 80,000 people, find the probability of the following:\r<BR>\n" );
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document.write( "a. 0 robberies\r<BR>\n" );
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document.write( "b. 1 robbery\r<BR>\n" );
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document.write( "c. 2 robberies\r<BR>\n" );
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document.write( "d. 3 or more robberies\r<BR>\n" );
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document.write( "part 4.\r<BR>\n" );
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document.write( "In a 400 page manuscript, there are 200 randomly distributed misprints. If a page is selected, find the probability that it has 1 misprint. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427900 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=427900\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.\r<BR>\n" );
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document.write( "Probability of event <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > that occurs:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28A%29+=+n%28A%29+%2F+n%28S%29 ALIGN=MIDDLE  ALT=\"P%28A%29+=+n%28A%29+%2F+n%28S%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28A%29+=+4+%2F+5 ALIGN=MIDDLE  ALT=\"P%28A%29+=+4+%2F+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28A%29+=+highlight%280.8%29 ALIGN=MIDDLE  ALT=\"P%28A%29+=+highlight%280.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Probability of event <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > that does not occur:\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" >(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >') = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+P%28A%29 ALIGN=MIDDLE  ALT=\"1+-+P%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" >(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >') = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-++0.8 ALIGN=MIDDLE  ALT=\"1+-++0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" >(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >')= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.2 ALIGN=MIDDLE  ALT=\"0.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "A copy machine randomly puts out 10 blank sheets per 500 copies processed. <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=10%2F500=highlight%280.02%29 ALIGN=MIDDLE  ALT=\"p=10%2F500=highlight%280.02%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the probability that in a run of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300+ ALIGN=MIDDLE  ALT=\"300+\"   DISABLED_style= \"max-width:90%; height:auto;\" >copies, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+ ALIGN=MIDDLE  ALT=\"5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >sheets of paper will be blank is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=5%2F300=0.016666666666666666666666666666667 ALIGN=MIDDLE  ALT=\"p=5%2F300=0.016666666666666666666666666666667\"   DISABLED_style= \"max-width:90%; height:auto;\" > &asymp; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=0.017%29 ALIGN=MIDDLE  ALT=\"highlight%28p=0.017%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Prob%28+a+robbery%29+=+20000%2F80000=1%2F4+=+0.25 ALIGN=MIDDLE  ALT=\"Prob%28+a+robbery%29+=+20000%2F80000=1%2F4+=+0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=80000 ALIGN=MIDDLE  ALT=\"n=80000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The Binomial distribution has the probability\r<BR>\n" );
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document.write( "function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x=r%29=+nCr+p%5Er+%281-p%29%5E%28n-r%29 ALIGN=MIDDLE  ALT=\"P%28x=r%29=+nCr+p%5Er+%281-p%29%5E%28n-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,.....,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nCr+=+n%21+%2F+%28r%21+%28n-r%29%21%29 ALIGN=MIDDLE  ALT=\"nCr+=+n%21+%2F+%28r%21+%28n-r%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80000 ALIGN=MIDDLE  ALT=\"80000\"   DISABLED_style= \"max-width:90%; height:auto;\" > people, we expect <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > robberies.\r<BR>\n" );
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document.write( "a)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=4%2F80000 ALIGN=MIDDLE  ALT=\"p=4%2F80000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1%2F20000 ALIGN=MIDDLE  ALT=\"p=1%2F20000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=0.00005%29 ALIGN=MIDDLE  ALT=\"highlight%28r=0.00005%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "use the source to compute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2880000C0%29%281%2F20000%29%5E0%2819999%2F20000%29%5E8000=+0.018 ALIGN=MIDDLE  ALT=\"%2880000C0%29%281%2F20000%29%5E0%2819999%2F20000%29%5E8000=+0.018\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using Poisson with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lambda+=4 ALIGN=MIDDLE  ALT=\"lambda+=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x=0%29=+e%5E-4+%2A%284%5E0+%2F+1%21%29=0.018%281%2F1%29=highlight%280.018%29 ALIGN=MIDDLE  ALT=\"P%28x=0%29=+e%5E-4+%2A%284%5E0+%2F+1%21%29=0.018%281%2F1%29=highlight%280.018%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=1%29 ALIGN=MIDDLE  ALT=\"highlight%28r=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using Poisson with lambda=4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E-4%284%5E1+%2F+1%21%29=0.018%2A4=highlight%280.072%29 ALIGN=MIDDLE  ALT=\"e%5E-4%284%5E1+%2F+1%21%29=0.018%2A4=highlight%280.072%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=3%29 ALIGN=MIDDLE  ALT=\"highlight%28r=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E-4+%284%5E3+%2F+3%21%29+=0.018%2A%2864%2F6%29=0.018%2A10.666666666666666666666666666667=+highlight%280.192%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d) \r<BR>\n" );
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document.write( "p( highlight(x >=3))= p( 3 through 20000)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=variance=np%281-p%29=3.99998 ALIGN=MIDDLE  ALT=\"variance=np%281-p%29=3.99998\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sd=1.99999 ALIGN=MIDDLE  ALT=\"sd=1.99999\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28+x+%3E=3%29+=+P%28+z+%3E%283-4%29%2F2%29+=+p%28+z+%3E+-0.5%29=highlight%280.6915%29 ALIGN=MIDDLE  ALT=\"P%28+x+%3E=3%29+=+P%28+z+%3E%283-4%29%2F2%29+=+p%28+z+%3E+-0.5%29=highlight%280.6915%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This uses normal approximation instead of Binomial because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is too large and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p ALIGN=MIDDLE  ALT=\"p\"   DISABLED_style= \"max-width:90%; height:auto;\" > is too small.\r<BR>\n" );
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document.write( "4.\r<BR>\n" );
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document.write( "Presuming there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200 ALIGN=MIDDLE  ALT=\"200\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400 ALIGN=MIDDLE  ALT=\"400\"   DISABLED_style= \"max-width:90%; height:auto;\" > total pages with misprints, there is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" >% probability of discovering one on any given page.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=200%2F400=1%2F2=0.50 ALIGN=MIDDLE  ALT=\"p=200%2F400=1%2F2=0.50\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2850%29 ALIGN=MIDDLE  ALT=\"highlight%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >%\r<BR>\n" );
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document.write( " </SPAN>\n" );
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