if s^2 = .04, then s = sqrt(.04) = .2
s is the standard deviation.
you have:
m =10.25
s = .2
you want to find the probability of the number of liters being 10 or less.
you calculate the z-factors as follows:
z = (x-m)/s
z is the z-factor
x is the raw score
m is raw mean
s is the standared deviation
you get z = (10 - 10.25) / .2
solve for z to get z = -.25 / .2 = -.125
use a z-score calculator or a z-score table to find the area to the left of a z-score of -.125.
i used the the following calculator.
http://stattrek.com/online-calculator/normal.aspx
i used the following table.
http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf
i entered a z-score of -.125.
the mean is and the standard deviation is 1 for a z-score.
the calculator then told me that the probability of getting a z-score to the left of that (less than that) was .45026
the calculator told me that the probability of a z-score being less than -.125 is .45026
with the table, i had to do a little interpolating.
this is because the table only goes to 2 decimal places.
i looked for the probability to the left of -.12 and to the left of -.13.
a z-score of -.12 gave an area to the left as .4522.
a z-score of -.13 gave an area to the left as .4483.
since -.125 is roughly in between, then i calculated that the probability would be .45025
the calculator is more accurate than interpolation because interpolation is straight line while the actual values in between are more on a curve.
here's a picture of what the calculator shows:
here's a picture of what the correct row on the table shows:
in the table, the first column gets you to the row that contains a z-score of -.1.
that's one decimal place accuracy only.
on that same row, the third column gets you the area to the left of a z-score of -.12 and the fourth column gets you to the area to the left of a z-score of -.13.
that's twodecimal place accuracy only.
you then interpolate to get the area to the left of a z-score of -.125