document.write( "Question 1206486: Jim is the team statistician. Based on the team's record so far, Jim estimates the probability of winning any given game is 0.54. Use a normal approximation to estimate the probability the team will win at least 16 of the season's scheduled 31 games. \n" ); document.write( "

Algebra.Com's Answer #844008 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "Jim is the team statistician. Based on the team's record so far, Jim estimates the probability
\n" ); document.write( "of winning any given game is 0.54. Use a normal approximation to estimate the probability
\n" ); document.write( "the team will win at least 16 of the season's scheduled 31 games.
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document.write( "The oroginal experiment is a Binomial, but we have an instruction to use a normal distribution\r\n" );
document.write( "as an approximation.\r\n" );
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document.write( "So, for the normal distribution we use the mean m = n*p = 0.54*31 = 16.74\r\n" );
document.write( "and the standard deviation SD =  =  = 2.775 (rounded).\r\n" );
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document.write( "After that, we calculate the estimate normal probability, using the standard function normcdf \r\n" );
document.write( "of the regular calculator TI-83/84\r\n" );
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document.write( "                 z1   z2   mean    SD              <<<---=== formatting pattern\r\n" );
document.write( "    P = normcdf(15.5,9999, 16.74, 2.775) = 0.6725.\r\n" );
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document.write( "Here the value 15.5 is the continuing correction factor, which serves as approximation for \"at least 16\".\r\n" );
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document.write( "ANSWER.  The estimated probability is 0.6725.\r\n" );
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