document.write( "Question 1199260: In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 522.7 kg and a variance of 100 kg squared. What is the probability that the weight of concrete poured into a mold is less than 521 kg? \n" ); document.write( "
Algebra.Com's Answer #833052 by ikleyn(52908)\"\" \"About 
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\n" ); document.write( "In a factory, the weight of the concrete poured into a mold by a machine
\n" ); document.write( "follows a normal distribution with a mean of 522.7 kg and a variance of 100 kg squared.
\n" ); document.write( "What is the probability that the weight of concrete poured into a mold is less than 521 kg?
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\n" ); document.write( "\n" ); document.write( "        The solution by @Theo is incorrect,  since  Theo mistakenly uses the value of 100 \r
\n" ); document.write( "\n" ); document.write( "        as the standard deviation in his calculations,  while the correct value\r
\n" ); document.write( "\n" ); document.write( "        for the standard deviation in this problem is   \"sqrt%28100%29\" = 10 kilograms.\r
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\n" ); document.write( "\n" ); document.write( "        So,  I came to bring a correct solution.\r
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document.write( "Every normal distribution curve is a bell shaped curve.\r\n" );
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document.write( "In this problem, they want you determine the area under this specific normal curve\r\n" );
document.write( "below the raw mark of 521 kg.  This area is the sought probability.\r\n" );
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document.write( "Go to web-site https://onlinestatbook.com/2/calculators/normal_dist.html\r\n" );
document.write( "and find there free of charge online calculator, specially developed for this purpose.\r\n" );
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document.write( "Input the mean value 522.7 and the standard deviation value of 10;\r\n" );
document.write( "input 521 in the window \"Below\"; then click \"Recalculate\".\r\n" );
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document.write( "You will get the ANSWER  0.4325  in the window \"Probability\".\r\n" );
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document.write( "The auxiliary plot will show you the area of the interest.\r\n" );
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document.write( "Now, when you know \"what to do\", I will tell you that you can get the same result \r\n" );
document.write( "using your calculator  TI-83 or TI-84 (or whatever).\r\n" );
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document.write( "For it, use the calculator' standard function normalcdf with parameters\r\n" );
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document.write( "                      z1    z2   mean   SD   \r\n" );
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document.write( "     P = normalcdf( -9999,  521, 522.7, 10) = 0.4325.\r\n" );
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document.write( "You will get the same value of the probability 0.4325 from your calculator.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the solution is completed.\r
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\n" ); document.write( "\n" ); document.write( "From my post, you learned two methods/approaches of solving such problems.\r
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