document.write( "Question 1185638: A gardener buys a package of seeds. Seventy-four percent of seeds of this
\n" ); document.write( "type germinate. The gardener plants 100 seeds. Approximate the
\n" ); document.write( "probability that 76 or more seeds germinate.
\n" ); document.write( "a. 0.5199
\n" ); document.write( "b.0.3669
\n" ); document.write( "c.0.4761
\n" ); document.write( "d.0.4840 \n" ); document.write( "

Algebra.Com's Answer #849571 by ikleyn(52943) $\"\"$ $\"About$

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\n" ); document.write( "A gardener buys a package of seeds. Seventy-four percent of seeds of this type germinate.
\n" ); document.write( "The gardener plants 100 seeds. Approximate the probability that 76 or more seeds germinate.
\n" ); document.write( "a. 0.5199
\n" ); document.write( "b.0.3669
\n" ); document.write( "c.0.4761
\n" ); document.write( "d.0.4840
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document.write( "The situation is a binomial experiment.\r\n" );
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document.write( "The number of trials is 100.  The individual probability of success in each individual trial is 0.74.\r\n" );
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document.write( "So, formally there are standard formulas for binomial distribution, but the Math does not \r\n" );
document.write( "recommend to use them, because the formulas include high degree exponents and too great binomial\r\n" );
document.write( "coefficients.  Instead, there is another, very effective and standard approach on solving such problems.\r\n" );
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document.write( "This approach is to use an appropriate normal distribution as an approximation to the Binomial distribution.\r\n" );
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document.write( "The relevant normal distribution has the mean  m = n*p = 100*0.74 = 74\r\n" );
document.write( "and the standard deviation  S =  =  = 4.386342.\r\n" );
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document.write( "This normal curve covers all 100 seeds on the horizontal axis, and we should take the area under\r\n" );
document.write( "this normal curve on the right of the threshold value of 76.\r\n" );
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document.write( "A convenient tool for it is to use the standard function  normcdf (which means Cumulative Distribution Function\r\n" );
document.write( "for normal distribution).  This function is in any regular calculator like TI-83/84.\r\n" );
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document.write( "So, you write/print in your calculator\r\n" );
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document.write( "                 z1     z2   mean    SD        <<<---===  formatting pattern.\r\n" );
document.write( "    P = normcdf(75.5,  9999,  74,  4.386342)\r\n" );
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document.write( "Here z1 = 75.5  stands for 76 and presents the continuing correction;  z2 stand for infinity on the horizontal axis,\r\n" );
document.write( "mean is the mean and SD is the standard deviation.\r\n" );
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document.write( "Then the function will return the probability, which you are looking for: P = 0.3662.\r\n" );
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document.write( "It is the ANSWER to the problem's question  P = 0.3662, obtained with the normal distribution approximation.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to learn more from the Internet about the normal distribution as an approximation for binomial distribution,\r
\n" ); document.write( "\n" ); document.write( "go to Google with these keywords \"normal distribution as an approximation for binomial distribution\"\r
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