This is exactly like question 1156138 which I answered earlier today. So I'll
just copy and paste it and change the numbers. Are you still not getting it?
If you have questions, just ask me in the space below and I'll get back to you
by email. No charge ever.
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 78 is in the middle. Then 78 plus the
standard deviation 11.4 is added over and over: 78+11.4=89.4 is the first number
marked right of the mean, then 89.4+11.4=100.8, etc. on the right of the mean 78,
and 78-11.4=66.6, then 66.6-11.4=55.2, etc. on the left of the mean 78.
Here is the x-axis of actual values which we denote by x or X:
32.4 43.8 55.2 66.6 78 89.4 100.8 111.2 123.6 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 = 85
We use the formula 
which we round off to -0.61, which means that the original x-value of
85 on the x-axis of the first graph above corresponds to the z-score
of -0.61 on the z-axis of the second graph above.
(b)
x = 95
We use the formula 
which we round off to 1.49, which means that the original x-value of
95 on the x-axis of the first graph above corresponds to the z-score
of 1.49 on the z-axis of the second graph above.
(c)
x = 50
We use the formula 
which we round off to -2.46, which means that the original x-value of
50 on the x-axis of the first graph above corresponds to the z-score
of -2.46 on the z-axis of the second graph above.
(d)
x = 75
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
