document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473251>Question 473251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a large survey, it was discovered that 1 out of every 5 adults visits disney world every year. if 30 adults are randomly selected, what is the probability that exactly 7 of them will visit disney world this year? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #324537 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=324537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a binomial distribution problem. Recall that the binomial pdf value is given by the formula\r<BR>\n" );
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document.write( "P(X = x) = (n C x)*(p^x)*(1-p)^(n-x)\r<BR>\n" );
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document.write( "In this case, n=30, p=1/5=0.2 and x=7.\r<BR>\n" );
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document.write( "So plug these values into the formula and evaluate\r<BR>\n" );
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document.write( "P(X = 7) = (30 C 7)*(0.2)^(7)*(1-0.2)^(30-7) \r<BR>\n" );
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document.write( "P(X = 7) = (30 C 7)*(0.2)^(7)*(0.8)^(30-7) \r<BR>\n" );
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document.write( "P(X = 7) = (2035800)*(0.2)^(7)*(0.8)^23 \r<BR>\n" );
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document.write( "Note: 30 C 7 = (30!)/(7!(30-7)!) = 2035800\r<BR>\n" );
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document.write( "P(X = 7) = (2035800)*(0.0000128)*(0.00590295810358705651712) \r<BR>\n" );
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document.write( "P(X = 7) =  0.1538206989732163796166770688\r<BR>\n" );
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document.write( "P(X = 7) =  0.1538\r<BR>\n" );
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document.write( "Question: what is the probability that exactly 7 of them will visit disney world this year?\r<BR>\n" );
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document.write( "Answer: Probability is approximately 0.1538, which is roughly 15.38% </SPAN>\n" );
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