document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978036>Question 978036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question text<BR>\n" );
document.write( "A wildlife biologist observes four brown bears as they attempt to catch salmon in a river in Alaska.  Assume that each bear has a .7 probability of catching a fish and that the bears fishing attempts are independent.  Let the random variable X be the number of bears that catch a fish.  Create the probability distribution for X (rounding each to THREE decimal places).\r<BR>\n" );
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document.write( "What is the standard deviation of the above distribution?  Round to three places.\r<BR>\n" );
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document.write( "Answer: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599529 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=599529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a binomial distribution problem\r<BR>\n" );
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document.write( "Use the formula <BR>\n" );
document.write( "(n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "where n = 4, p = 0.7 and k ranges from k = 0 to k = 4\r<BR>\n" );
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document.write( "Let's calculate the probabilities\r<BR>\n" );
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document.write( "when k = 0, the probability is...<BR>\n" );
document.write( "(n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "(4 C 0)*(0.7)^(0)*(1-0.7)^(4-0)<BR>\n" );
document.write( "0.0081<BR>\n" );
document.write( "0.008\r<BR>\n" );
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document.write( "when k = 1, the probability is...<BR>\n" );
document.write( "(n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "(4 C 1)*(0.7)^(1)*(1-0.7)^(4-1)<BR>\n" );
document.write( "0.0756<BR>\n" );
document.write( "0.076\r<BR>\n" );
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document.write( "when k = 2, the probability is...<BR>\n" );
document.write( "(n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "(4 C 2)*(0.7)^(2)*(1-0.7)^(4-2)<BR>\n" );
document.write( "0.2646<BR>\n" );
document.write( "0.265\r<BR>\n" );
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document.write( "when k = 3, the probability is...<BR>\n" );
document.write( "(n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "(4 C 3)*(0.7)^(3)*(1-0.7)^(4-3)<BR>\n" );
document.write( "0.4116<BR>\n" );
document.write( "0.412\r<BR>\n" );
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document.write( "when k = 4, the probability is...<BR>\n" );
document.write( "(n C k)*(p)^(k)*(1-p)^(n-k)<BR>\n" );
document.write( "(4 C 4)*(0.7)^(4)*(1-0.7)^(4-4)<BR>\n" );
document.write( "0.2401<BR>\n" );
document.write( "0.240\r<BR>\n" );
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document.write( "Let's wrap all this up into a neat distribution table\r<BR>\n" );
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document.write( "<tr><th>k</th><th>P(X = k)</th></tr><tr><TD >0</TD><TD >0.008</TD></tr><tr><TD >1</TD><TD >0.076</TD></tr><tr><TD >2</TD><TD >0.265</TD></tr><tr><TD >3</TD><TD >0.412</TD></tr><tr><TD >4</TD><TD >0.240</TD></tr>\n" );
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document.write( "The standard deviation is equal to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%2Ap%2A%281-p%29%29+=+sqrt%284%2A0.7%2A%281-0.7%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28n%2Ap%2A%281-p%29%29+=+sqrt%284%2A0.7%2A%281-0.7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%2Ap%2A%281-p%29%29+=+0.91651513899117 ALIGN=MIDDLE  ALT=\"sqrt%28n%2Ap%2A%281-p%29%29+=+0.91651513899117\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28n%2Ap%2A%281-p%29%29+=+0.917 ALIGN=MIDDLE  ALT=\"sqrt%28n%2Ap%2A%281-p%29%29+=+0.917\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The standard deviation is approximately 0.917 </SPAN>\n" );
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