document.write( "Question 1202101: It is known that 82% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 61 new products, find the following probabilities. (Round your answers to four decimal places.) Find this on a TI-83\r
\n" ); document.write( "\n" ); document.write( "1) within 2 years 47 or more fail\r
\n" ); document.write( "\n" ); document.write( "2) within 2 years 58 or fewer fail\r
\n" ); document.write( "\n" ); document.write( "3) within 2 years 15 or more succeed\r
\n" ); document.write( "\n" ); document.write( "4) within 2 years fewer than 10 succeed \n" ); document.write( "

Algebra.Com's Answer #836740 by ikleyn(52908) $\"\"$ $\"About$

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\n" ); document.write( "It is known that 82% of all new products introduced in grocery stores fail
\n" ); document.write( "(are taken off the market) within 2 years. If a grocery store chain
\n" ); document.write( "introduces 61 new products, find the following probabilities.
\n" ); document.write( "(Round your answers to four decimal places.) Find this on a TI-83
\n" ); document.write( "(1) within 2 years 47 or more fail
\n" ); document.write( "(2) within 2 years 58 or fewer fail
\n" ); document.write( "(3) within 2 years 15 or more succeed
\n" ); document.write( "(4) within 2 years fewer than 10 succeed
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document.write( "The original problem is, of course, a binomial distribution type.\r\n" );
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document.write( "But the number of trials is great: 61.\r\n" );
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document.write( "In such cases, the traditional approach is not to use the binomial distribution formula.\r\n" );
document.write( "The traditional approach is to use the normal distribution as an approximation\r\n" );
document.write( "to the binomial distribution.\r\n" );
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document.write( "This normal distribution has the mean value n*p = 61*0.82 = 50.02 and the \r\n" );
document.write( "standard deviation  =  = 3.0006 (rounded).\r\n" );
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document.write( "(1)  So, in question (1), our goal is to find the area under this normal curve on the right of the \r\n" );
document.write( "     raw mark 47;  more precisely, taking the continuity correction factor, on the right\r\n" );
document.write( "     of the raw mark 46.5.  You can use regular calculator TI-83 \r\n" );
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document.write( "                       z1    z2    mean    SD      <<<---===  formatting pattern\r\n" );
document.write( "        P = normalcdf(46.5, 9999, 50.02, 3.0006).\r\n" );
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document.write( "     You get the ANSWER  0.8796  (rounded)\r\n" );
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document.write( "(2)  In question (2), our goal is to find the area under this normal curve on the left of the \r\n" );
document.write( "     raw mark 58;  more precisely, taking the continuity correction factor, on the left\r\n" );
document.write( "     of the raw mark 58.5.  You can use regular calculator TI-83\r\n" );
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document.write( "                       z1     z2    mean    SD      <<<---===  formatting pattern\r\n" );
document.write( "        P = normalcdf(-9999, 58.5, 50.02, 3.0006).\r\n" );
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document.write( "     You get the ANSWER  0.9976  (rounded).\r\n" );
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document.write( "(3)  \"within 2 years 15 or more succeed\".\r\n" );
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document.write( "     Hence, the rest of the new products, or less than 61-15=46 of the new products, will fail.\r\n" );
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document.write( "     P(within 2 years 15 or more succeed) = P(less than 61-15=46 of the new products will fail)\r\n" );
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document.write( "                        z1    z2    mean    SD      <<<---===  formatting pattern\r\n" );
document.write( "        P = normalcdf(-9999, 45.5, 50.02, 3.0006).\r\n" );
document.write( "     \r\n" );
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document.write( "     The ANSWER  is  0.066  (rounded).\r\n" );
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document.write( "(4)  \"within 2 years fewer than 10 succeed\".\r\n" );
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document.write( "     Hence, the rest of the new products, or at least 61-10=51 of the new products, will fail.\r\n" );
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document.write( "     P(within 2 years fewer than 10 succeed) = P(at least 61-10=51 of the new products, will fail)\r\n" );
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document.write( "                       z1    z2    mean    SD      <<<---===  formatting pattern\r\n" );
document.write( "        P = normalcdf(50.5, 9999, 50.02, 3.0006).\r\n" );
document.write( "     \r\n" );
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document.write( "     The ANSWER  is  0.4365  (rounded).\r\n" );
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