document.write( "Question 630051: A fair coin tossed 64 times. Find the probability of getting 32 to 40 heads inclusive \n" ); document.write( "

Algebra.Com's Answer #852475 by n3(4) $\"\"$ $\"About$

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\n" ); document.write( "A fair coin tossed 64 times. Find the probability of getting 32 to 40 heads inclusive
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\n" ); document.write( "\n" ); document.write( "        Clearly, this problem is originally on Binomial distribution.\r
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\n" ); document.write( "\n" ); document.write( "        But the number of trials, which is 64, in this problem is very big.\r
\n" ); document.write( "\n" ); document.write( "        When it is so big, the standard recommendations instruct to use normal distribution \r
\n" ); document.write( "\n" ); document.write( "        as an approximation to the binomial distribution.\r
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\n" ); document.write( "\n" ); document.write( "        So, it is assumed, by default, that the solution will be made using a normal distribution as an approximation.\r
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document.write( "The corresponding normal distribution has the mean equal to n*p = 64*(1/2) = 32\r\n" );
document.write( "and the standard deviation SD =  =  =  = 4.\r\n" );
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document.write( "To be accurate, we should introduce and account for the continuity factor and calculate p(31.5 <= n <= 40.5).\r\n" );
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document.write( "For this calculation, I use a regular calculator TI-84/87, standard function normcfd\r\n" );
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document.write( "                                    z1    z2  mean SD  <<<---=== formatting pattern\r\n" );
document.write( "    p(31.5 <= n <= 40.5) = normcfd(31.5, 40.5, 32,  4).\r\n" );
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document.write( "It gives the answer  p = 0.5329.\r\n" );
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document.write( "I confirmed it using the online free of charge calculator for normal distribution at this site\r\n" );
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document.write( "https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
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document.write( "ANSWER.  The probability is  0.5329.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in a way as it is expected to be done.\r
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\n" ); document.write( "\n" ); document.write( "This my solution is to replace the @Theo' solution.\r
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