document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=517777>Question 517777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An FBI survey showed that for about 80% of property crimes, criminals are never found and the case is never solved.  Suppose that in a particular neighborhood there are repeated property crimes.  The police are investigating six property crimes in this neighborhood.<BR>\n" );
document.write( ".  what is the probability that none of the crimes will be solved? .028<BR>\n" );
document.write( "b.  what is the probability that at least one will be solved? .972<BR>\n" );
document.write( "c.  what is the probability that 4 or more will not be solved? <BR>\n" );
document.write( "d.  what is the expected number of crimes that will be solved and what is the std. deviation?<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 #344909 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=344909\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An FBI survey showed that for about 80% of property crimes, criminals are never found and the case is never solved. Suppose that in a particular neighborhood there are repeated property crimes. The police are investigating six property crimes in this neighborhood.<BR>\n" );
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document.write( "Binomial Problem with n = 6 and p(not solved) = 0.8 p(solved) = 0.2<BR>\n" );
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document.write( "a. what is the probability that none of the crimes will be solved? <BR>\n" );
document.write( "P(x = 0) = 0.8^6 = 0.2621<BR>\n" );
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document.write( "b. what is the probability that at least one will be solved? <BR>\n" );
document.write( "(x>= 1) = 1 - P(x = 0) = 1 - 0.2621 = 0.7379\r<BR>\n" );
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document.write( "c. what is the probability that 4 or more will not be solved?<BR>\n" );
document.write( "P(4<= x <=6) = 1 - P(0<= x <=3) = 1 - binomcdf(6,0.8,3) = 0.9011<BR>\n" );
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document.write( "d. what is the expected number of crimes that will be solved and what is the std. deviation?<BR>\n" );
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document.write( "E(x) = u = np = 6*0.2 = 1.2 <BR>\n" );
document.write( "std = sqrt[npq] = sqrt(1.2*0.8] = 0.9798<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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