SOLUTION: if you have a normal distribution of 200 and a standard deviation of 25 what percent of data points fall above 125

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Question 1188412: if you have a normal distribution of 200 and a standard deviation of 25 what percent of data points fall above 125
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
mean is 200.
standard deviation is 25.

if you use a calculator, like the one at https://davidmlane.com/hyperstat/z_table.html, you'll get the answer very quickly.

here are the results from using that calculator.



the area to the right of 125 is equal to .9987 rounded to 4 decimal places, as shown on the calculator.

multiply that by 100 to get 99.87%.

if you use the ti-85 plus, you'll get the same answer with more detail in just about the same amount of time, maybe a touch bit longer.

the answer is .9986500328.

round that off to 4 decimal digits to get .9987.

multiply it by 100 to get 99.87%.

if you use the z-score table, such as the one at https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf, it takes a little longer and a bit more analysis.

you would use the z-score formula of:

z = (x - m) / s

z is tghe z=score
x is the raw score of 125
m is the mean of 200
s is the standard deviation of 25

the formula becomes:

z = (125 - 200) / 25.

solve for z to get:

z = -3.

look into the z-score table to find that the area to the left of a z-score of -3 is equal to .00135.

the area to the right of that z-score is equal to 1 minus .00135 = .99865.
multiply that by 100 to get 99.865%

round that off to 4 decimal places to get .9987.

multiply it by 100 to get 99.87% .

all sources agree when you round to 4 decimal places.