document.write( "Question 1202083: What are the chances that a person who is murdered actually knew the murderer? The answer to this question explains why a lot of police detective work begins with relatives and friends of the victim! About 68% of people who are murdered actually knew the person who committed the murder. Suppose that a detective file in New Orleans has 59 current unsolved murders. Find the following probabilities with a TI-83 calculator
\n" ); document.write( "1) at least 35 of the victims knew their murderers
\n" ); document.write( "2) at most 48 of the victims knew their murderers
\n" ); document.write( "3) fewer than 30 victims did not know their murderers
\n" ); document.write( "4) more than 20 victims did not know their murderers \n" ); document.write( "

Algebra.Com's Answer #836725 by ikleyn(52832) $\"\"$ $\"About$

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\n" ); document.write( "What are the chances that a person who is murdered actually knew the murderer?
\n" ); document.write( "The answer to this question explains why a lot of police detective work begins
\n" ); document.write( "with relatives and friends of the victim! About 68% of people who are murdered
\n" ); document.write( "actually knew the person who committed the murder. Suppose that a detective file
\n" ); document.write( "in New Orleans has 59 current unsolved murders. Find the following probabilities
\n" ); document.write( "with a TI-83 calculator
\n" ); document.write( "1) at least 35 of the victims knew their murderers
\n" ); document.write( "2) at most 48 of the victims knew their murderers
\n" ); document.write( "3) fewer than 30 victims did not know their murderers
\n" ); document.write( "4) more than 20 victims did not know their murderers
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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: 59.\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 = 59*0.68 = 40.12 and the \r\n" );
document.write( "standard deviation  =  = 3.583071308 (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 35;  more precisely, taking the continuity correction factor, on the right\r\n" );
document.write( "     of the raw mark 34.5.  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(34.5, 9999, 40.12, 3.583071308).\r\n" );
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document.write( "     You get the ANSWER  0.9416  (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 48;  more precisely, taking the continuity correction factor, on the left\r\n" );
document.write( "     of the raw mark 48.5.  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, 48.5, 40.12, 3.583071308).\r\n" );
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document.write( "     You get the ANSWER  0.9903  (rounded).\r\n" );
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document.write( "(3)  \"fewer than 30 victims did not know their murderers\".\r\n" );
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document.write( "     Hence, the rest of the victims, or at least 59-29=30 of the victims, knew their murderers.\r\n" );
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document.write( "     P(fewer than 30 victims did not know their murderers) = P(at least 59-29=30 of the victims knew their murderers)\r\n" );
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document.write( "                       z1    z2    mean    SD      <<<---===  formatting pattern\r\n" );
document.write( "        P = normalcdf(29.5, 9999, 40.12, 3.583071308).\r\n" );
document.write( "     \r\n" );
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document.write( "     The ANSWER  is  0.9985  (rounded).\r\n" );
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document.write( "(4)  \"more than 20 victims did not know their murderers\".\r\n" );
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document.write( "     Hence, the rest of the victims, or at most 59-20-1=38 of the victims, knew their murderers.\r\n" );
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document.write( "     P(more than 20 victims did not know their murderers) = P(at most 59-20-1=38 of the victims knew their murderers)\r\n" );
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document.write( "                       z1     z2    mean    SD      <<<---===  formatting pattern\r\n" );
document.write( "        P = normalcdf(-9999, 38.5, 40.12, 3.583071308).\r\n" );
document.write( "     \r\n" );
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document.write( "     The ANSWER  is  0.3256  (rounded).\r\n" );
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