Question 1188412
mean is 200.
standard deviation is 25.


if you use a calculator, like the one at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>, you'll get the answer very quickly.


here are the results from using that calculator.


<img src = "http://theo.x10hosting.com/2021/120403.jpg" >


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 <a href = "https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf" target = "_blank">https://www.rit.edu/academicsuccesscenter/sites/rit.edu.academicsuccesscenter/files/documents/math-handouts/Standard%20Normal%20Distribution%20Table.pdf</a>, 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.