document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165713>Question 1165713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) The probability of being a smoker among a group of cases with lung cancer is 0.75. Calculate the probability that in a group of 6 cases, you have atleast 3 smokers.<BR>\n" );
document.write( "b) What are the expected value and variance of the number of smokers?<BR>\n" );
document.write( "c) The number of babies born in a day at a hospital's maternity wing follows a Poisson distribution with a mean of 4 in a day. Calculate the probability that five babies are born during a particular day in this maternity wing.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852961 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53339)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852961\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "a) The probability of being a smoker among a group of cases with lung cancer is 0.75. <BR>\n" );
document.write( "   Calculate the probability that in a group of 6 cases, you have at least 3 smokers.\r<BR>\n" );
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document.write( "b) What are the expected value and variance of the number of smokers?\r<BR>\n" );
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document.write( "c) The number of babies born in a day at a hospital's maternity wing follows a Poisson distribution <BR>\n" );
document.write( "   with a mean of 4 in a day. Calculate the probability that five babies are born during a particular day <BR>\n" );
document.write( "   in this maternity wing.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In the post by &nbsp;@CPhill, &nbsp;his calculations in part &nbsp;(a) &nbsp;are &nbsp;INCORRECT.\r<BR>\n" );
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document.write( "For example, he calculates in part (a)\r\n" );
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document.write( "    P(X=3) = binom{6}{3}*(0.75)^3*(0.25)^{3} = 20 \times 0.421875 \times 0.015625 \approx 0.032959\r\n" );
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document.write( "which is wrong.\r\n" );
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document.write( "The correct calculation in this case is\r\n" );
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document.write( "    P(X=3) = C(6,3)*0.75^3*0.25^3 = 20*0.75^3*0.25^3 = 0.131835938,\r\n" );
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document.write( "and then his wrong contribution of P(X=3) goes into his final answer to part (a).\r\n" );
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document.write( " </SPAN>\n" );
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