You are asked to change from numbers on the x-axis on the first graph below
to their corresponding numbers on the z-axis on the second graph below.
On the first graph below, the mean 214 is in the middle. Then 214 plus the
standard deviation 48 is added over and over: 214+48=262 is the first number
marked right of the mean, then 262+48=310, etc. on the right of the mean 214,
and 214-48=166, then 166-48=118, etc. on the left of the mean 214.
Here is the x-axis of actual values which we denote by x or X:
22 70 118 166 214 262 310 358 406 x
We change the values of the actual x-axis values to the z-axis values below,
which we call "z-scores" of the x-values above on the x-axis. The z-scores on
the z-axis below are the codings of the original x-values that tell us how many
times the standard deviation is added to or subtracted from the mean in the
actual x-value to get the z-score corresponding to that x-value.
-4 -3 -2 -1 0 1 2 3 4 z
(a)
x = 200
We use the formula 
which we round off to -0.29, which means that the original x-value of
200 on the x-axis of the first graph above corresponds to the z-score
of -0.29 on the z-axis of the second graph above.
(b)
x = 224
We use the formula 
which we round off to -0.21, which means that the original x-value of
224 on the x-axis of the first graph above corresponds to the z-score
of -0.21 on the z-axis of the second graph above.
(c)
x = 300
We use the formula 
which we round off to 1.79, which means that the original x-value of
300 on the x-axis of the first graph above corresponds to the z-score
of 1.79 on the z-axis of the second graph above.
(d)
x = 100
You do that one yourself. And please learn HOW to calculate the z-score,
and ESPECIALLY, learn what it MEANS. They call it the "z-axis" and the
values on it "z-scores" because it has "zero" corresponding to the mean
value and "zero" begins with "z".
Edwin
