document.write( "Question 1205385: Eggs are packed into cartons of six. A sample of 90 cartons is randomly
\n" ); document.write( "selected and the number of damaged eggs in each carton counted.
\n" ); document.write( "Number of damaged eggs
\n" ); document.write( "0
\n" ); document.write( "1
\n" ); document.write( "2
\n" ); document.write( "3
\n" ); document.write( "4
\n" ); document.write( "5
\n" ); document.write( "6\r
\n" ); document.write( "\n" ); document.write( "Number of Cartons
\n" ); document.write( "52
\n" ); document.write( "15
\n" ); document.write( "8
\n" ); document.write( "5
\n" ); document.write( "4
\n" ); document.write( "3
\n" ); document.write( "3\r
\n" ); document.write( "\n" ); document.write( "Does the number of damaged eggs in a carton follow a Binomial distribution?
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Algebra.Com's Answer #842146 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "Eggs are packed into cartons of six. A sample of 90 cartons is randomly
\n" ); document.write( "selected and the number of damaged eggs in each carton counted.
\n" ); document.write( "
\r\n" );
document.write( "Number of damaged eggs\r\n" );
document.write( "0\r\n" );
document.write( "1\r\n" );
document.write( "2\r\n" );
document.write( "3\r\n" );
document.write( "4\r\n" );
document.write( "5\r\n" );
document.write( "6\r\n" );
document.write( "\r\n" );
document.write( "Number of Cartons\r\n" );
document.write( "52\r\n" );
document.write( "15\r\n" );
document.write( "8\r\n" );
document.write( "5\r\n" );
document.write( "4\r\n" );
document.write( "3\r\n" );
document.write( "3\r\n" );
document.write( "

\n" ); document.write( "Does the number of damaged eggs in a carton follow a Binomial distribution?
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\n" ); document.write( "\n" ); document.write( "Let assume for a minute that the given distribution is a binomial with the probability of a successful outcome
\n" ); document.write( "(success in this problem is getting a damaged egg)  at each individual trial   p = const.\r
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\n" ); document.write( "\n" ); document.write( "Then the probability to have 6 successful trials (six damaged eggs in a cartoon) is   \"p%5E6\" = \"3%2F90\" = \"1%2F30\",
\n" ); document.write( "which implies   p = \"root%286%2C1%2F30%29\" = 0.5673   (approximately).\r
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\n" ); document.write( "\n" ); document.write( "From the other side,  the probability to have 0 successful trials  (no damaged eggs in a cartoon)  is   \"%281-p%29%5E6\" = \"52%2F90\" = \"26%2F45\",
\n" ); document.write( "which implies   1-p = \"root%286%2C26%2F45%29\" = 0.9126   (approximately).\r
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\n" ); document.write( "\n" ); document.write( "But then we have this contradiction: \r
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\n" ); document.write( "\n" ); document.write( "        the sum of  p  and ( 1-p),   which is   0.5673 + 0.9126 ~ 1.4700,   is  FAR  from to be equal  1  (one).\r
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\n" ); document.write( "\n" ); document.write( "From this reasoning,  my conclusion is that the given distribution  IS  NOT  a binomial.\r
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