document.write( "Question 1072652: 2. Using the unit normal table, find the proportion under the standard normal curve that lies in the tail for each of the following:\r
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document.write( "a. z = 1.00
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document.write( "b. z = -1.05
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document.write( "c. z = 0
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document.write( "d. z = 2.80
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document.write( "e. z = 1.96
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Algebra.Com's Answer #687505 by Edwin McCravy(20054)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "I'll just do e. Hopefully you can do the others by yourself.\r\n" ); document.write( "They're all similar.\r\n" ); document.write( "\r\n" ); document.write( "There are several different kinds of standard normal tables. \r\n" ); document.write( "If yours is like this one, \r\n" ); document.write( "\r\n" ); document.write( "http://math.arizona.edu/~rsims/ma464/standardnormaltable.pdf\r\n" ); document.write( "\r\n" ); document.write( "Which has negative and positive values for z. (Be sure to scroll \r\n" ); document.write( "all the way down to see the whole table:\r\n" ); document.write( "\r\n" ); document.write( "then for z=1.96\r\n" ); document.write( "\r\n" ); document.write( "Find 1.9 in the z-column on the left, go horizontally across from there\r\n" ); document.write( "to what's below the column headed .06\r\n" ); document.write( "\r\n" ); document.write( "That number that you read is .97500. But that's not the answer.\r\n" ); document.write( "That's the area to the left of 1.96. To get the area to the right\r\n" ); document.write( "of 1.96, which is in the tail you must subtract from 0.5 and get \r\n" ); document.write( "1.0-0.97500 and get 0.02500. \r\n" ); document.write( "\r\n" ); document.write( "A shortcut is to realize that because the normal curve is\r\n" ); document.write( "symmetrical, and therefore the area to the right of +1.96 is the same as \r\n" ); document.write( "the area to the left of -1.96. So just go to -1.9 and across under .06\r\n" ); document.write( "and read 0.02500 directly. \r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "If you have this kind of table:\r\n" ); document.write( "\r\n" ); document.write( "http://www.mathsisfun.com/data/standard-normal-distribution-table.html\r\n" ); document.write( "\r\n" ); document.write( "which has z=0 and 0.00000 in the upper left corner. (Scroll down to the\r\n" ); document.write( "table).\r\n" ); document.write( "\r\n" ); document.write( "Find 1.9 in the z-column on the left, go horizontally across from there\r\n" ); document.write( "to what's below the column headed 0.06\r\n" ); document.write( "\r\n" ); document.write( "That number that you read is 0.4750. But that's not the answer.\r\n" ); document.write( "That's the area between the middle of the curve and 1.96. To get the\r\n" ); document.write( "area to the right of 1.96, which is in the tail you must subtract from \r\n" ); document.write( "0.5 and get 0.5-0.4750 and get 0.0250. \r\n" ); document.write( "\r\n" ); document.write( "Edwin \n" ); document.write( " \n" ); document.write( " |