document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1140089>Question 1140089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that x has a Poisson distribution with mu equals 9​, what is the probability that x equals 3​? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #760576 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=760576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the poisson probability formula is:\r<BR>\n" );
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document.write( "p(x) = m^x * e^(-m) / x!\r<BR>\n" );
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document.write( "m is the mean<BR>\n" );
document.write( "x is the desired number that you want the probability for.<BR>\n" );
document.write( "e is the scientific constant equal to 2.718281828.....\r<BR>\n" );
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document.write( "when m = 9 and x = 3,the formula becomes;\r<BR>\n" );
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document.write( "p(3) = 9^3 * e^(-9) / 3! = .01499 rounded to 4 decimal digits.\r<BR>\n" );
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document.write( "there is an online calculator that does the dirty work for you.\r<BR>\n" );
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document.write( "in addition, that calculator gives you much more than just the probability of exactly x occurrences.\r<BR>\n" );
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document.write( "that calculator can be found at <a  rel=nofollow HREF= \"https://www.algebra.com/tutors/faq.mpl\" target = \"_blank\">https://www.algebra.com/tutors/faq.mpl</a>\r<BR>\n" );
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document.write( "here's a display of the results from that calculator dealing with your problem.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/042901.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "here's a reference that tells you what the poisson probability distribution is and how to work with it.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://stattrek.com/probability-distributions/poisson.aspx\" target = \"_blank\">https://stattrek.com/probability-distributions/poisson.aspx</a>\r<BR>\n" );
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document.write( "note that the formula, shown as:\r<BR>\n" );
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document.write( "p(x) = m^x * e^(-m) / x!\r<BR>\n" );
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document.write( "m is the mean<BR>\n" );
document.write( "x is the desired number that you want the probability for.<BR>\n" );
document.write( "e is the scientific constant equal to 2.718281828.....\r<BR>\n" );
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document.write( "can also be shown as:\r<BR>\n" );
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document.write( "p(x) = m^x / (e^m * x!)\r<BR>\n" );
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document.write( "that's because e^(-m) is the same as 1 / e^m.\r<BR>\n" );
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document.write( "note that the calculator not only gives you p(x = 3).\r<BR>\n" );
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document.write( "it also gives you p(x < 3), p(x <= 3), p(x > 3), p(x >= 3).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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