if you find the z-score for the left tail, then the same z-score with the opposite sign will be the z-score for the right tail.
specifically.
30% is in the middle which means 70% / 2 = 35% is in the left tail.
you look for a z-score that has .35 of the area under the normal distribution curve to the left of it.
that z-score will be -.385 rounded to 3 decimal places.
that will be the low z-score.
the high z-score will be +.385 rounded to 3 decimal places.
you can use the online z-score calculator at http://davidmlane.com/hyperstat/z_table.html
you would use the value from an area portion of this calculator and you would look for the z-score that has .30 area between.
the calculator will then tell you the lower and upper z-score bounds for that area.
a display of the results are shown below.
you would do a similar analysis for the middle 42%.
58% in the tails divided by 2 = 29% in the left tail and 29% in the right tail.
the z-score with an area of .29 under the normal distribution curve to the left of it would be a z-score of -.553 rounded to 3 decimal places.
the low z-score is -.553
the high z-score is +.553
using the same online z-score calculator, the display of the results are shown below.
i used the inverse norm function of the TI-84 Plus to find the z-score from the area.
if you need help understanding how to do that by using the normal distribution tables, let me know and i'll take you through it.
use of a calculator is far easier and more accurate.
one such online calculator can be found at https://stattrek.com/online-calculator/normal.aspx
give it a try.
if you can't find the left hand z-score using this calculator, let me know and i'll take you through it.