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 #396703 by AnlytcPhil(1806) $\"\"$ $\"About$

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A fair coin tossed 64 times. Find the probability of getting 32 to 40 heads inclusive
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document.write( "The first tutor forgot to subtract .5 from the lower bound and to add .5\r\n" );
document.write( "to the upper bound when using the normal to approximate the binomial.\r\n" );
document.write( "The second tutor got it correct using Excel to do the calculations.  In fact\r\n" );
document.write( "it is probably more accurate than below, but I think your teacher intended you\r\n" );
document.write( "to use the following method.\r\n" );
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document.write( "You're probably supposed to use the normal approximation, as the first tutor\r\n" );
document.write( "assumed but she forgot about the \".5\". \r\n" );
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document.write( "Calculate the mean = n×p = 64×.5 = 32\r\n" );
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document.write( "Standard deviation =  =  = 4\r\n" );
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document.write( "Then calculate the z-scores for x = 31.5 and 40.5.  (we subtract .5 from\r\n" );
document.write( "the lower bound 32 and add .5 to the upper bound 40).\r\n" );
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document.write( "z =  =  = -.125 round to hundredths -.13 \r\n" );
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document.write( "z =  =  = 2.125 round to hundredths 2.13\r\n" );
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document.write( "We look those z-values up in the normal table. Depending on which kind of\r\n" );
document.write( "normal table you have, you do one of these: \r\n" );
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document.write( "  subtract .9834 - .4483 = .5351  if your table has negative values of z.      \r\n" );
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document.write( "or you add .0517 + .4834 = .5351  if your table has only positive z values.\r\n" );
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document.write( "Either way the answer is .5351\r\n" );
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document.write( "Edwin

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