document.write( "Question 1171498: The Agency for Healthcare Research and Quality reported that 53% of people who had coronary bypass surgery in a recent year were over the age of 65. Fifteen coronary bypass patients are sampled.
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Algebra.Com's Answer #796405 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "It is a binomial distribution type problem, where the probability under the question is the sum\r\n" );
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document.write( "     P = P(fewer than 8 of 15) = P(0) + P(1) + P(2) + . . .  + P(7) =       (1)\r\n" );
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document.write( "The number of trials is              15;\r\n" );
document.write( "The indexes of success trials        k = 0,1,2,3, . . . ,7\r\n" );
document.write( "The probability of success trial     p = 0.53;\r\n" );
document.write( "                                     q = 1 - p\r\n" );
document.write( "C(n,k) = n! / (k! * (n-k)!)          are binomial coefficients.\r\n" );
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document.write( "The sum  (1)  is a cumulative sum.\r\n" );
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document.write( "Instead of calculating every term of (1) individually and then summing them up, you may use Excel function \r\n" );
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document.write( "BINOM.DIST(7, 15, 0.53, TRUE)  to calculate the cumulative sum value in one click.\r\n" );
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document.write( "In this way,  you get\r\n" );
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document.write( "    P =  = 0.406524.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On Excel function BINOM.DIST, see its description everywhere, for example\r
\n" ); document.write( "\n" ); document.write( "https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c\r
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\n" ); document.write( "\n" ); document.write( "On binompdf function for pocket calculators TI-83 and TI-84 see the link\r
\n" ); document.write( "\n" ); document.write( "http://users.rowan.edu/~schultzl/ti/binomial.pdf\r
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\n" ); document.write( "\n" ); document.write( "If you want to see other similar solved problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solving problems on Binomial distribution \r
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