document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011720>Question 1011720</A>: <I><SPAN STYLE=\"word-break: break-all;\">  If the probability of being a smoker among a group of cases with lung cancer is .6, what’s the probability that in a group of 8 cases you have less than 2 smokers? More than 5? What are the expected value and variance of the number of smokers?  </SPAN>\n" );
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document.write( "Question:<BR>\n" );
document.write( " If the probability of being a smoker among a group of cases with lung cancer is .6, what’s the probability that in a group of 8 cases you have less than 2 smokers? More than 5? What are the expected value and variance of the number of smokers? <BR>\n" );
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document.write( "Solution:<BR>\n" );
document.write( "The problem can be solved using the binomial distribution, with p=0.6.<BR>\n" );
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document.write( "For n=8,<BR>\n" );
document.write( "P(X<2)=P(X=0)+P(X=1)<BR>\n" );
document.write( "=C(8,0)*p^0*(1-p)^8 + C(8,1)*p^1*(1-p)^(8-1)<BR>\n" );
document.write( "=0.0065536+0.0078643<BR>\n" );
document.write( "=0.008520<BR>\n" );
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document.write( "P(X>5)=P(X=6)+P(X=7)+P(X=8)<BR>\n" );
document.write( "=0.2090+0.0896+0.0168<BR>\n" );
document.write( "=0.3154<BR>\n" );
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document.write( "Expected value = np=8*0.6=4.8<BR>\n" );
document.write( "Variance = npq=8*0.6*(1-0.6)=1.92 </SPAN>\n" );
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