document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=920902>Question 920902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following question is a Hypergeometric Distribution.\r<BR>\n" );
document.write( "\n" );
document.write( "x~Hypergeometric(N=110, r=24, n=15) where \"N\" is the population size, \"r\" is the number of successes in population, and \"n\" is the sample size. I have answered (a), (b), and (c), using their respected formulas, the answers are provided. I am struggling with part (d). I am not looking for the exact numerical answer, but rather the way to go about answering it. \r<BR>\n" );
document.write( "\n" );
document.write( "A biologist captures 24 grizzly bears during the spring, and fits each with a radio collar. At the end of summer, the biologist is to observe 15 grizzly bears from a helicopter, and count the number that are radio collared. This count is represented by the random variable X. \r<BR>\n" );
document.write( "\n" );
document.write( "Suppose there are 110 grizzly bears in the population. \r<BR>\n" );
document.write( "\n" );
document.write( "(a) What is the probability that of the 15 grizzly bears observed, 5 had radio collars? Use four decimals in your answer. \r<BR>\n" );
document.write( "\n" );
document.write( "P(X=5)= 0.128 \r<BR>\n" );
document.write( "\n" );
document.write( "(b) Find the probability that between 3 and 7 (inclusive) of the 15 grizzly bears observed were radio collared? \r<BR>\n" );
document.write( "\n" );
document.write( "P(3&#8804;X&#8804;7)= P(X&#8804;7)-P(X&#8804;2) = 0.6806 (use four decimals) \r<BR>\n" );
document.write( "\n" );
document.write( "(c) How many of the 15 grizzly bears observe from the helicopter does the biologist expect to be radio-collared? Provide the standard deviation as well. \r<BR>\n" );
document.write( "\n" );
document.write( "E(X)= 3.27 (use two decimals) \r<BR>\n" );
document.write( "\n" );
document.write( "SD(X)= 1.49 (use two decimals) \r<BR>\n" );
document.write( "\n" );
document.write( "(d) The biologist gets back from the helicopter observation expedition, and was asked the question: How many radio collared grizzly bears did you see? The biologist cannot remember exactly, so responds \" somewhere between 5 and 9 (inclusive) \". \r<BR>\n" );
document.write( "\n" );
document.write( "- I interpreted this information to be : P(5&#8804;X&#8804;9), which is P(X&#8804;9)-P(X&#8804;4) = 0.20014\r<BR>\n" );
document.write( "\n" );
document.write( "Given this information, what is the probability that the biologist saw 7 radio-collared grizzly bears? \r<BR>\n" );
document.write( "\n" );
document.write( "- As for calculating X=7, how is the above information P(5&#8804;X&#8804;9) relevant?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558618 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558618\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d) observation,<BR>\n" );
document.write( "7 is halfway between 5 and 9, therefore<BR>\n" );
document.write( "probability that the biologist saw 7 radio-collared grizzly bears = 0.20014 / 2 = 0.10007\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );