document.write( "Question 1207936: Sixty five percent of 12th graders attend school in a particular urban district. If a sample of 450 12th grade children is selected. Find the probability that more than 280 are actually enrolled in the school. \n" ); document.write( "

Algebra.Com's Answer #846079 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Sixty five percent of 12th graders attend school in a particular urban district.
\n" ); document.write( "If a sample of 450 12th grade children is selected.
\n" ); document.write( "Find the probability that more than 280 are actually enrolled in the school.
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document.write( "They want you find the probability that in the sample of 450\r\n" );
document.write( "12th grade children 280 attend school, if the individual probability is p = 0.65.\r\n" );
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document.write( "The original probability is the Binomial distribution, but since the sample \r\n" );
document.write( "is very big, it is recommended to use the normal distribution approximation.\r\n" );
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document.write( "For such approximation, the mean of the normal distribution is\r\n" );
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document.write( "    m = n*p = 450*0.65 = 292.5;\r\n" );
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document.write( "the standard deviation\r\n" );
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document.write( "    SD =  =  = 10.118  (rounded).\r\n" );
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document.write( "So now for this normal distribution we want to find the probability of having X >= 280.\r\n" );
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document.write( "For calculations, you may use your calculator (function normcdf), or Excel spreadsheet (function NORMDIST);\r\n" );
document.write( "or online calculator https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
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document.write( "Do not forget to use the continuity correction factor.\r\n" );
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document.write( "So, for a regular calculator TI-83/84, the function is\r\n" );
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document.write( "                 z1     z2    m      SD    <<<---===  formatting pattern\r\n" );
document.write( "    p = normcdf(279.5, 9999, 292.5, 10.118)\r\n" );
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document.write( "Here  z1 = 279.5  is the continuity correction factor for 280.\r\n" );
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document.write( "The  ANSWER  is  p = 0.9006  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you are a beginner student in learning probability distributions, I advise you to start learning
\n" ); document.write( "this kind of computations using the online calculator, to which I referred above.\r
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\n" ); document.write( "\n" ); document.write( "It provides a graphical support, so at each step you do understand what you are doing.
\n" ); document.write( "In addition, this graphical support prevents you from making mistakes.\r
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\n" ); document.write( "\n" ); document.write( "When you learn enough this kind of computations, you can switch to your regular calculator,
\n" ); document.write( "but even then you may use the online calculator for checking purposes.\r
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