document.write( "Question 968685: Using the standard normal distribution chart, find the probabilities in the following problems.\r
\n" ); document.write( "\n" ); document.write( "P(0 < z < 1.68)\r
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\n" ); document.write( "\n" ); document.write( "P(z > 1.39)\r
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\n" ); document.write( "\n" ); document.write( "P(-1.65 < z < 2.47)\r
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\n" ); document.write( "\n" ); document.write( "P(z < 2.23) \n" ); document.write( "
Algebra.Com's Answer #591899 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Using the standard normal distribution chart, find the probabilities in the following problems.
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document.write( "Go to this site to find a standard normal distribution chart:\r\n" );
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document.write( "https://www.easycalculation.com/statistics/normal-ztable.php\r\n" );
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document.write( "The table on that page gives area between z=0 and whatever z-score you have.\r\n" );
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\n" ); document.write( "P(0 < z < 1.68)
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document.write( "Find 1.6 in the left-most column on that page headed z.\r\n" );
document.write( "Go across to the next to last column headed 0.08 and read 0.4545\r\n" );
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document.write( "That's the answer: 0.4545\r\n" );
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\n" ); document.write( "P(z > 1.39)
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document.write( "Find 1.3 in the left-most column on that page headed z.\r\n" );
document.write( "Go across to the very last column headed 0.09 and read 0.4177\r\n" );
document.write( "But that's not the answer. That's the area between z=0 and z=1.39.\r\n" );
document.write( "The entire area to the right of z=0 is 0.5, so to find the area\r\n" );
document.write( "to the right of 1.39, we subtract 0.4177 from 0.5:\r\n" );
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document.write( " 0.5000\r\n" );
document.write( "-0.4177\r\n" );
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document.write( " 0.0823\r\n" );
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\n" ); document.write( "P(-1.65 < z < 2.47)
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document.write( "You must do that in two parts:\r\n" );
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document.write( "P(-1.65 < z < 0)  and P(0 < z < 2.47) and add them together.\r\n" );
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document.write( "First part: P(-1.65 < z < 0)\r\n" );
document.write( "By  symmetry, P(-1.65 < z < 0) is the same as P(0 < z < 1.65)\r\n" );
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document.write( "Find 1.6 in the left-most column on that page headed z.\r\n" );
document.write( "Go across to the column headed 0.05 and read 0.4505\r\n" );
document.write( "But that's only the left part of the answer, the area between \r\n" );
document.write( "z=-1.65 and z=0.\r\n" );
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document.write( "Second part: P(0 < z < 2.47)\r\n" );
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document.write( "Find 2.4 in the left-most column on that page headed z.\r\n" );
document.write( "Go across to the column headed 0.07 and read 0.4932\r\n" );
document.write( "That's the left right part of the answer, the area between \r\n" );
document.write( "z=0 and z=2.47.  We must add those together:\r\n" );
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document.write( " 0.4505\r\n" );
document.write( "+0.4932\r\n" );
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document.write( " 0.9437\r\n" );
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\n" ); document.write( "P(z < 2.23)
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document.write( "Find 2.2 in the left-most column on that page headed z.\r\n" );
document.write( "Go across to the column headed 0.03 and read 0.4871\r\n" );
document.write( "But that's not the answer. That's the area between z=0 and z=2.23.\r\n" );
document.write( "The entire area to the left of z=0 is 0.5, so to find the entire\r\n" );
document.write( "area to the left of 2.23, we must add 0.5 to 0.4871:\r\n" );
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document.write( " 0.4871\r\n" );
document.write( "+0.5000\r\n" );
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document.write( " 0.9871\r\n" );
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document.write( "Edwin
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