document.write( "Question 487066: Find the normal approximation for the binomial probability that x = 5, where n = 12 and p = 0.7. Compare this probability to the value of P(x=5) found in Table 2 of Appendix B in your textbook. \n" ); document.write( "

Algebra.Com's Answer #332952 by Theo(13342) $\"\"$ $\"About$

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n = 12
\n" ); document.write( "x = 5
\n" ); document.write( "p = .7
\n" ); document.write( "q = 1 - .7 = .3
\n" ); document.write( "p is probability of success
\n" ); document.write( "q is probability of failure
\n" ); document.write( "p(x) = nCx * p^x * q^(n-x)
\n" ); document.write( "for x = 5 and n = 12, this becomes:
\n" ); document.write( "p(5) = 12C5 * (.7)^5 * (.3)^7 which becomes:
\n" ); document.write( "p(5) = 792 * .16807 * .0002187 which becomes:
\n" ); document.write( "p(5) = .029111472\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "nCx is the combination formula of n! / (x! * (n-x)!))\r
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\n" ); document.write( "\n" ); document.write( "the probabilities for x = 1 to x = 12 are shown below.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "p	0.7\r\n" );
document.write( "q	0.3\r\n" );
document.write( "n	12\r\n" );
document.write( "x	p(x)\r\n" );
document.write( "0	5.31441E-07\r\n" );
document.write( "1	1.48803E-05\r\n" );
document.write( "2	0.000190964\r\n" );
document.write( "3	0.001485279\r\n" );
document.write( "4	0.007797716\r\n" );
document.write( "5	0.029111472   *****  p(x = 5)\r\n" );
document.write( "6	0.079247896\r\n" );
document.write( "7	0.158495792\r\n" );
document.write( "8	0.231139696\r\n" );
document.write( "9	0.239700426\r\n" );
document.write( "10	0.167790298\r\n" );
document.write( "11	0.071183763\r\n" );
document.write( "12	0.013841287\r\n" );
document.write( "	\r\n" );
document.write( "	1             total probability equals 1 (as it should)\r\n" );
document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "this should be approximately equal to the probability found in your textbook.
\n" ); document.write( "if not, let me know what is in table 2 of appendix b in your notebook.\r
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\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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