document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=405417>Question 405417</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
document.write( "\n" );
document.write( "I don't know if any of you answer statistics questions, but you really helped this struggling old lady get through algebra last year so I thought I would give you a try.  (Yes, I'm struggling with Stats just as much.)\r<BR>\n" );
document.write( "\n" );
document.write( "My question reads: A fisherman arrives at his favorite fishing spot. From past experience he knows that the number of fish he catches per hour follows a Poisson distribution at .5/hr. What’s the probability that will catch at least 3 in four hrs.\r<BR>\n" );
document.write( "\n" );
document.write( "Here's my take:  If he catches .5 in one hour, that makes the lambda .5/1?  Multiplied by the time (4 hours) gives me 2.  So I believe my 2 calculator numbers are 2 and 3.  If I'm doing the keystrokes correctly, I come up with a .184 probability.  \r<BR>\n" );
document.write( "\n" );
document.write( "Am I even in the ballpark?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks so much for ANY help you can give me!<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #286341 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=286341\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It depends on the parameter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha ALIGN=MIDDLE  ALT=\"alpha\"   DISABLED_style= \"max-width:90%; height:auto;\" > that you use.\r<BR>\n" );
document.write( "\n" );
document.write( "The probability mass function for the Poisson distribution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+e%5E%28-alpha%29%2A%28alpha%5Ex%2Fx%21%29 ALIGN=MIDDLE  ALT=\"p%28x%29+=+e%5E%28-alpha%29%2A%28alpha%5Ex%2Fx%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The parameter  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+=+2 ALIGN=MIDDLE  ALT=\"alpha+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is correct.<BR>\n" );
document.write( "The probability of catching 0, or 1, or 2 fish is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28-2%29%2A%282%5E0%2F0%21%29+%2B++e%5E%28-2%29%2A%282%5E1%2F1%21%29+%2B+e%5E%28-2%29%2A%282%5E2%2F2%21%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.  Hence the probability of catching at least 3 fish is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-%28+e%5E%28-2%29%2A%282%5E0%2F0%21%29+%2B++e%5E%28-2%29%2A%282%5E1%2F1%21%29+%2B+e%5E%28-2%29%2A%282%5E2%2F2%21%29%29=+5e%5E%28-2%29+=+0.676676+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >, to 6 decimal places. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );