Question 1174294
your mean is 70 and your standard deviation is 10.
you want to know the probability of getting a score between 65 and 85 if i understand you correctly.


using my ti-85 plus calculator, i got the same probability that you did as .6246553.


if you use the normal distribution tables, you would do the following.


first you want to find the z-score for 65 and 85 with a mean of 70 and a standard deviation of 10


the z-score formula is:
z = (x - m) / s
for x = 65, this formula becomes z = (65 - 70) / 10 = 1.5
for x = 85, this formula becomes z = (85 - 70) / 10 = -.5


you go to the z-score table to find the area to the left of 1.5 and the area to the left of -.5.
you will get area to the left of z-score of -.5 = .30854 and area to the left of z-score of 1.5 = .93319.
subtract the smaller area from the larger area to get .62465.


if you round to 3 decimal, the calculator gets you .625 and the table gets you .625.


if you truncate to 3 decimal places, you will get .624.


your calculator results of .6246553 will be equal to .625 when you round to 3 decimal places.


outside of the rounding discrepancy, the results i gave you pretty much agree with what your calculator gave you.


if i rounded .93319 to 3 decimal places, it would be equal to .933.
if i rounded .30854 to 3 decimal places, it would be equal to .309.
subtract .309 from .933 and you will get .624.


if you used the stattrek online calculator, that calculator rounds the probability to 3 decimal places.
that would explain the discrepancy.


the table i used can be found at <a href = "https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf" target = "_blank">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>


let me know if this answers your question and whether this is enough for you to understand how to do it.


theo