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.