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\n" ); document.write( "Question:
\n" ); document.write( "p(z>c)=.2546
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\n" ); document.write( "Solution:
\n" ); document.write( "Z is a standard normal variable usually available on calculators or standard tables. The function has a domain of (-∞,+∞), and it looks like the following:
\n" ); document.write( "The value of c can be read as 0.6601.
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\n" ); document.write( "In the case of a table, which are normally given to the left tail, as shown:
\n" ); document.write( "http://isites.harvard.edu/fs/docs/icb.topic1499785.files/Public%20Domain%20Normal%20Distribution%20Table.pdf
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\n" ); document.write( "Since we need the right tail (Z>c), we subtract the value 0.2546 from one to get 0.7454, and look up the value from the table, which corresponds to the value 0.66, as shown in red.
\n" ); document.write( "
\n" ); document.write( "It is possible to calculate the value to a higher precision using statistical software such as R. The commands to use could be:
\n" ); document.write( "qnorm(0.2546,lower.tail=FALSE);
\n" ); document.write( "or
\n" ); document.write( "qnorm(1-0.2546)
\n" ); document.write( "for the same reasons as explained using the table.
\n" ); document.write( "The latter statement makes use of the fact that the upper tail is the complement of the lower, hence subtract from one.
\n" ); document.write( "The result R gives is 0.6600839, as follows:\r
\n" ); document.write( "\n" ); document.write( "> qnorm(0.2546,lower.tail=FALSE)
\n" ); document.write( "[1] 0.6600839
\n" ); document.write( "> qnorm(1-0.2546)
\n" ); document.write( "[1] 0.6600839
\n" ); document.write( "> \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "