document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945987>Question 945987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A southern pine forest is known to be infested with pine bark beetles. It is known that 30 percent of the trees are so infested. A forester walks through the forest and selects at random 40 trees and tests to see if they have the infestation. what is the probability that of the 40 trees:<BR>\n" );
document.write( "1. four trees are infested?<BR>\n" );
document.write( "2. four of five trees are infested?<BR>\n" );
document.write( "3. at least three trees are infested?<BR>\n" );
document.write( "4. what are the mean and the variance of the distribution?<BR>\n" );
document.write( "5. can the distribution by approximated by a normal distribution?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577080 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=577080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A southern pine forest is known to be infested with pine bark beetles. It is known that 30 percent of the trees are so infested. A forester walks through the forest and selects at random 40 trees and tests to see if they have the infestation. what is the probability that of the 40 trees:<BR>\n" );
document.write( "Binomial Problem with n = 40 and p(infested) = 0.3<BR>\n" );
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document.write( " 1. four trees are infested?<BR>\n" );
document.write( "P(x = 4) = 40C4*0.3^4*0.7^37 = binompdf(40,0.3,4) = 0.00196<BR>\n" );
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document.write( " 2. four of five trees are infested?<BR>\n" );
document.write( "P(x = 4) = 5C4*0.3^4*0.7 = binompdf(5,0.3,4) = 0.02835<BR>\n" );
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document.write( " 3. at least three trees are infested? (out of 5 trees)<BR>\n" );
document.write( "P(3<= x <=5) = 1 - binomcdf(5,0.3,2) = 1-0.8369 = 0.1631<BR>\n" );
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document.write( " 4. what are the mean and the variance of the distribution?<BR>\n" );
document.write( "mean = np = 5*0.3 = 1.5<BR>\n" );
document.write( "std = sqrt[npq] = sqrt[1.5*0.7] = 1.02<BR>\n" );
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document.write( " 5. can the distribution by approximated by a normal distribution? <BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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