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yes it is.
\n" ); document.write( "the middle .80 of the distribution curve will have a lower z-score and an upper z-score bounding it.
\n" ); document.write( "the normal distribution curve has 100% of the area underneath it.
\n" ); document.write( "if you are looking for the middle 80%, then 10% will be to the left of the lower z-score and 10% will be to the right of the higher z-score.
\n" ); document.write( "in the following pictures:
\n" ); document.write( "the first picture shows the shaded area in the middle equal to 80%.
\n" ); document.write( "the second picture shows the shaded area to the left equal to 10%.
\n" ); document.write( "the third picture shows the shaded area to the right equal to 10%.
\n" ); document.write( "note that 80% = .8, and 10% = .10
\n" ); document.write( "note also that .0999999999 is effectively .10 once you round it.
\n" ); document.write( "any discrepancies are due to rounding because the inputs to the software that shows you the picture doesn't accept more than 4 or 5 decimal digits of accuracy.
\n" ); document.write( "here's the pictures.
\n" ); document.write( "look below the picture for more comments.
\n" ); document.write( "
![\"$$$\"](\"http://theo.x10hosting.com/2016/050901.jpg\")
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![\"$$$\"](\"http://theo.x10hosting.com/2016/050902.jpg\")
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![\"$$$\"](\"http://theo.x10hosting.com/2016/050903.jpg\")
\n" ); document.write( "if you are looking for the z-score in the z-score table, the procedure would be something like this:
\n" ); document.write( "1 - .8 = .20.
\n" ); document.write( "that's the sum of the area to the left and right of the middle.
\n" ); document.write( "divide that by 2 to get .10
\n" ); document.write( "that's the area to the left and it's also the area to the right.
\n" ); document.write( "the simplest way to find the z-score is to find .10 in the z-score table that represents the area to the left of the z-score.
\n" ); document.write( "find that z-score.
\n" ); document.write( "in the table i used, a z-score of -1.28 shows .1003 area to the left of it and a z-score of -1.29 shows .0985 area to the left of it.
\n" ); document.write( "without interpolating, you would show a z-score of -1.28 since the area to the left of it is closer to .1 then the area to the left of -1.29.
\n" ); document.write( "if you are using a calculator, like the ti-84+, your answer would be -1.281551567.
\n" ); document.write( "as you can see, it's closer to -1.28 than -1.29.
\n" ); document.write( "since the normal distribution curve is symmetric around the mean, 10% to the left of a z-score of -1.281551567 will also give you 10% to the right of a z-score of 1.281551567.
\n" ); document.write( "to find that, look for an area of .9 to the left of the z-score indicated.
\n" ); document.write( "you will find that a z-score of 1.28 has an area of .8997 to the left of it and a z-score of 1.29 has an area of .9015 to the left of it.
\n" ); document.write( "you will also find that the area to the left of the z-score of 1.28 is closer to .9 than the area to the left of the z-score of 1.29.
\n" ); document.write( "if you use your calculator to find the area of .9 to the left of the z-score, it will tell you that the z-score is equal to 1.281551567.
\n" ); document.write( "you can see that in the pictures above, even though the z-score numbers have been rounded.
\n" ); document.write( "the z-score tablei used can be found here:
\n" ); document.write( "http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
\n" ); document.write( "the z-score calculator that drew the pictures i showed you can be found here:
\n" ); document.write( "http://davidmlane.com/hyperstat/z_table.html \n" ); document.write( "