SOLUTION: Find the z-score boundaries that separate a normal distribution as described in each of the following. The middle 30% from the 70% in the tails. The middle 42% from the 58%

Algebra ->  Probability-and-statistics -> SOLUTION: Find the z-score boundaries that separate a normal distribution as described in each of the following. The middle 30% from the 70% in the tails. The middle 42% from the 58%      Log On


   



Question 1142646: Find the z-score boundaries that separate a normal distribution as described in each of the following.
The middle 30% from the 70% in the tails.
The middle 42% from the 58% in the tails.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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 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.