document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199410>Question 1199410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4.4.2 Suppose that over a period of several years the average number of deaths from a certain noncontagious disease has been 10. If the number of deaths from this disease follows the Poisson distribution, what is the probability that during the current year: a. Exactly seven people will die from the disease? b. Ten or more people will die from the disease? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848457 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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=848457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Probability of Exactly Seven Deaths**\r<BR>\n" );
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document.write( "* **Poisson Distribution Formula:**<BR>\n" );
document.write( "   P(X = k) = (λ^k * e^(-λ)) / k! <BR>\n" );
document.write( "   where:<BR>\n" );
document.write( "       * X is the number of occurrences (deaths)<BR>\n" );
document.write( "       * λ is the average number of occurrences (10)<BR>\n" );
document.write( "       * k is the specific number of occurrences (7)<BR>\n" );
document.write( "       * e is the base of the natural logarithm (approximately 2.71828)\r<BR>\n" );
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document.write( "* **Calculate:**<BR>\n" );
document.write( "   P(X = 7) = (10^7 * e^(-10)) / 7! <BR>\n" );
document.write( "   P(X = 7) ≈ 0.0901\r<BR>\n" );
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document.write( "* **Probability of exactly seven deaths: 0.0901 or 9.01%**\r<BR>\n" );
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document.write( "**b) Probability of Ten or More Deaths**\r<BR>\n" );
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document.write( "* **Calculate the probability of fewer than ten deaths:**<BR>\n" );
document.write( "   P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9) \r<BR>\n" );
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document.write( "   * Calculate each probability using the Poisson formula as in part (a).\r<BR>\n" );
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document.write( "* **Probability of ten or more deaths:**<BR>\n" );
document.write( "   P(X ≥ 10) = 1 - P(X < 10) \r<BR>\n" );
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document.write( "* **Using a Poisson probability table or calculator:**<BR>\n" );
document.write( "   P(X ≥ 10) ≈ 0.5830\r<BR>\n" );
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document.write( "* **Probability of ten or more deaths: 0.5830 or 58.30%**\r<BR>\n" );
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document.write( "**Note:**\r<BR>\n" );
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document.write( "* You can use statistical software (like R, Python, or Excel) or online calculators to calculate Poisson probabilities more efficiently.<BR>\n" );
document.write( "* The Poisson distribution assumes that events are independent and occur at a constant average rate.<BR>\n" );
document.write( " </SPAN>\n" );
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