document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4857>Question 4857</A>: <I><SPAN STYLE=\"word-break: break-all;\">  An insect trap catches an average of four insects per 20 minute. Assuming that insects are caught randomly and independently, what is the probability that in a randomly chosen 20 minute period:<BR>\n" );
document.write( "A) exactly five insects will be caught?<BR>\n" );
document.write( "B) no more than two insects will be caught?<BR>\n" );
document.write( "c) at least four insects will be caught?<BR>\n" );
document.write( "D) over a randomly chosen one hour period what is the probability that exactly 10 insects will be caught?\r<BR>\n" );
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document.write( "The body temperature of a population of mammals are known to be normally distributed with a mean of 37.2 degrees and a standard deviation of 0.35 degress.<BR>\n" );
document.write( "A) what proportion of the population have a tempreture of <BR>\n" );
document.write( "i) more than 39 degrees ?<BR>\n" );
document.write( "ii) less than 36.8 degrees?<BR>\n" );
document.write( "iii) between 36.5 degrees and 38.5 degrees?\r<BR>\n" );
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document.write( "I will be very grateful if you could help me with these questions please. <BR>\n" );
document.write( "Thank you very much<BR>\n" );
document.write( "Birgul....<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 #2379 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=2379\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Looks like the 1st question is related to Poission Distribution.<BR>\n" );
document.write( " Every 20 min, lambda = 4. Let the random varible be X with <BR>\n" );
document.write( " (I) Poission Distribution with mean Lambda = 4. <BR>\n" );
document.write( " Pr(X =k) = (Lambda^k/k!) *e^(-Lambda) <BR>\n" );
document.write( " A) exactly five insects will be caught?<BR>\n" );
document.write( " B) no more than two insects will be caught?<BR>\n" );
document.write( " c) at least four insects will be caught?<BR>\n" );
document.write( " D) over a randomly chosen one hour period what is the probability that exactly <BR>\n" );
document.write( " 10 insects will be caught? <BR>\n" );
document.write( " Sol: A)  Lambda = 4, k= 5, Pr(X = 5) = (4^5/5!) *e^(-4) = 0.156<BR>\n" );
document.write( "      B)  Lambda = 4, Pr(X <= 2) = 0.238<BR>\n" );
document.write( "      C)  Lambda = 4, Pr(X => 4) = 1 - Pr(X <= 3) = 0.567<BR>\n" );
document.write( "      D) When time = 1 hr = 3*20 min, the mean Lambda is 3*4 = 12 .<BR>\n" );
document.write( "       Lambda = 12, Pr(X = 10) = 0.105\r<BR>\n" );
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document.write( " (II) Mu mean = 37.2 and a standard deviation sigma = 0.35 degress.<BR>\n" );
document.write( "  Convert it to the dstandard normal distribution by<BR>\n" );
document.write( "  z = (X- 37.2)/0.35 and look up the table to find the probability\r<BR>\n" );
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document.write( " i) more than 39 degrees ?<BR>\n" );
document.write( "  X = 39, Pr(X> 39)=1- NORMDIST(39,37.2,0.35,1) = 1.35541E-07<BR>\n" );
document.write( " <BR>\n" );
document.write( " ii) less than 36.8 degrees?<BR>\n" );
document.write( "  X = 36.8, Pr(X< 36.8)= NORMDIST(36.8,37.2,0.35,1) = 0.127<BR>\n" );
document.write( "iii) between 36.5 degrees and 38.5 degrees? <BR>\n" );
document.write( "  Pr(36.5 < X< 38.5)= Pr( X< 38.5) - Pr( X< 36.5)<BR>\n" );
document.write( "  = 0.98\r<BR>\n" );
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document.write( " Suggestion : Use MS Excel or Tables in the textbook.\r<BR>\n" );
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document.write( " Kenny<BR>\n" );
document.write( "  </SPAN>\n" );
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