document.write( "Question 87622This question is from textbook DISCOVERING STATISTICS
\n" ); document.write( ": 4. find the value of z such that .80 of the area under the curve lies between -z and z \n" ); document.write( "
Algebra.Com's Answer #63545 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "4. find the value of z such that .80 of the area under the curve lies \r\n" );
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document.write( "Start with this normal curve,\r\n" );
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document.write( "we are trying to find where the middle 80% of the area starts and\r\n" );
document.write( "stops, as indicated by the area between these two line segments:\r\n" );
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document.write( "Therefore there is 20% of the area which is not between those two\r\n" );
document.write( "values. Due to symmetry, 10% will be left of the lower value and\r\n" );
document.write( "the other 10% will be right of the upper value.  So now we have:\r\n" );
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document.write( "Now I don't know what kind of normal table you have in your book,\r\n" );
document.write( "as there are two kinds currently in use, or whether you're not \r\n" );
document.write( "using a table at all but using a TI-83 or TI-84 or similar \r\n" );
document.write( "graphical calculator.\r\n" );
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document.write( "In one kind of table, there are negative values given for z.  If \r\n" );
document.write( "you have that kind of table, you'll just look through the body of \r\n" );
document.write( "the table and find the value closest to .1000.  The closest you \r\n" );
document.write( "find is .1003, where z = -1.28.  So the answer to the question \r\n" );
document.write( "is 1.28, and the middle 80% of the area will extend all the way \r\n" );
document.write( "from -1.28 to +1.28.\r\n" );
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document.write( "If you have the other kind of table, where negative values for z \r\n" );
document.write( "are not given, then you have to look through the body of your \r\n" );
document.write( "table to find the closest z-value for half the area, or .4.  The \r\n" );
document.write( "closest you can find to .4 is .3997, which corresponds to a \r\n" );
document.write( "z-value of 1.28. It's the area between the y-axis and the upper \r\n" );
document.write( "bound of the area, which is half of the total area. \r\n" );
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document.write( "If you're using a TI-83 or TI-84 then\r\n" );
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document.write( "From the cleared main screen\r\n" );
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document.write( "PRESS 2nd VARS ---    for DISTR\r\n" );
document.write( "PRESS 3        ---    on the screen you see InvNorm(\r\n" );
document.write( "Type .1)       ---    on the screen you see InvNorm(.1)\r\n" );
document.write( "Press ENTER    ---    on the screen you see -1.281551567\r\n" );
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document.write( "That's the lower value so the upper value in 1.281551567.\r\n" );
document.write( "Rounded off to two decimal places, z = 1.28, same as with\r\n" );
document.write( "tables.\r\n" );
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document.write( "Edwin
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