SOLUTION: For each of the following, determine the z score that divides the distribution such that the given percentage of scores lies above the z score(round to two decimal places):

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Question 1186954: For each of the following, determine the z score that divides the distribution such that the given percentage of scores lies above the z score(round to two decimal places):
a. 50% b. 2.50% c. 5% d. 30% e. 80% f. 90%
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
a normal distribution calculator is the easiest way to find this.
most z-score tables give you the area to the left of the z-score.
the area to the right of the z-score is equal to 1 minus the area to the left of the z-score.
some calculators give you the area to the left of the z-score and the area to the right of the z-score, as well as the area between z-scores.
those are the easiest calculators to use.

your hardest option is to use the z-score table.
that requires you to find the z-score manually.

i'll go the easiest way first and then come back and do it the harder way and then the hardest way.

the easiest way is to use the calculator at https://davidmlane.com/hyperstat/z_table.html

here are your results from using this calculator.

all you need to do is round these answers to two decimal places.

for example, 1.645 becomes 1.65.

the next easiest way is to use a calculator that only gives you the area to the left of the z-score.

one such calculator can be found at https://stattrek.com/online-calculator/normal.aspx

for examle, this calculator will find the z-score for the area to the left ot it.

if the area to the right is .9, then the area to the left is 1 minus that = .1.

find the area to the left equal to .1 and you have automatically found the area to the right of .9.

here are the results from using that calculator to find the area to the right equal to .9.

as you can see, the z-score with the area of .1 to the left of it is the same as the z-score with the area of .9 to the right of it.

the hardest way to find the z-score is to use the z-score table.

the z-score table i used can be found at https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf

finding the z-score to the nearest 2 decimal places is not that bad.
finding the z-score to any more decimal places than that becomes a chore.

using that table, i found that:

area to the left of .10027 gives a z-score of -1.28
area to the left of .09853 gives a z-score of -1.29

area to the left that i want is .1.
.10027 minus .1 = .00027
.1 minus .09853 = .00147.
.10027 is closer to .1 than .09853.
that says the z-score is -1.28.

not the hardest job in the world, but certainly harder than using the calculators.