document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469405>Question 469405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please show me how to solve this statistic? Thank you!\r<BR>\n" );
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document.write( "Does crime pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solved. Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetuated by the same criminals. The police are investigating three property crime cases in this district.\r<BR>\n" );
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document.write( "1.What is the probability that none of the crimes will ever be solved? (Use 3 decimal places.)\r<BR>\n" );
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document.write( "2.What is the probability that at least one crime will be solved? (Use 3 decimal places.)\r<BR>\n" );
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document.write( "3.What is the expected number of crimes that will be solved? What is the standard deviation? (Use 2 decimal places.)\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 #322070 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=322070\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> *********************************<BR>\n" );
document.write( "1. Each crime has 20% chance of being solved<BR>\n" );
document.write( "They want you to use Binomial Theorem:<BR>\n" );
document.write( "P(x) = nCx*p^x*(1-p)^n-x<BR>\n" );
document.write( "where p is probability of solving crime, n is number of crimes, and x is theoretical number of crimes solved<BR>\n" );
document.write( "p = 0.2<BR>\n" );
document.write( "n = 3<BR>\n" );
document.write( "x = 0<BR>\n" );
document.write( "P(0) = (0.8)^3 = 0.512<BR>\n" );
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document.write( "2. Similar to above,<BR>\n" );
document.write( "Find P(x>0) = P(1)+P(2)+P(3)<BR>\n" );
document.write( "To save time, note that all possible probabilities must sum to 1<BR>\n" );
document.write( "So P(x>0) = 1 - P(0) = 1 - .512 = .488<BR>\n" );
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document.write( "3. E(X) = n*p<BR>\n" );
document.write( "V(X) = n*p*(1-p)<BR>\n" );
document.write( "where E(X) is mean or expected value and V(X) is variance<BR>\n" );
document.write( "Standard deviation is just the square root of variance<BR>\n" );
document.write( "n=3<BR>\n" );
document.write( "p=0.2<BR>\n" );
document.write( "E(X) = 3*.2 = 0.6<BR>\n" );
document.write( "sqrt(V(X)) = sqrt(3*.2*.8) = 0.693<BR>\n" );
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