Question 1142646
if 70% is in the tails, then half of that is in the left tail and half of that is in the right tail.


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 <a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


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.


<img src = "http://theo.x10hosting.com/2019/062705.jpg" alt="$$$" >


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.


<img src = "http://theo.x10hosting.com/2019/062706.jpg" alt="$$$" >


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 <a href = "https://stattrek.com/online-calculator/normal.aspx" target = "_blank">https://stattrek.com/online-calculator/normal.aspx</a>


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.