alpha = 1 - .8 = .2
alpha / 2 = .1
that is the area to the left of the z-score on the low side of the confidence level and the area to the right of the z-score on the high side of the confidence level.
to find the area to the left of the low side z-score, you would look up an area of .1 in the z-score table and get the closest z-score.
to find the area to the right of the high side z-score, you would find the area of 1 - .1 = .9 in the z-score table and get the closest z-score.
i used the following table.
https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf
the table tells you the area to the left of a z-score.
the unit digit and the first decimal digit of the z-score are in the row indicated by the left hand column.
the second decimal digit is in the column on that row indicated by the top row.
for example:
z-score of 1.28 would show 1.2 in the left hand column on the indicated row.
the .08 that is added to it to make 1.28 would show on the top row of the indicated column.
i found.
area of .89973 gave a z-score of 1.28
are of .90147 gave z-score of 1.29.
1.28 was the closest so i chose that.
area of .10027 gave a z-score of -1.28
area of .09853 gave a z-score of -1.29
-1.28 was the closest so i chose that.
since the normal distribution table is symmetric about the mean, i only needed to find the low side z-score.
the high side z-score would be the with with a revered sign.
the results of that inquiry are shown below.
i also used the following normal distribution calculator.
http://davidmlane.com/hyperstat/z_table.html
in this calculator, i chose to find the z-score from the area and put in an area of.8 (the confident level) and chose between.
it gave me the same answer with much less effort on my part and with greater accuracy.
note that an area of .8 was the confidence level and the area in between left an area of .1 to the left of it and an area of .1 to the right of it which was my alpha / 2 that i calculated earlier.
the result of that inquiry are shown below.
