We are given a fixed number of samples, n = 100.
We are given two conditions:
x = 45, z = 0.50
x = 52, z = 1.00
The relevant equation we can use here is:
z = (x – m) / s
where m is the mean and s is the std dev
So for the two conditions:
0.50 = (45 – m) / s --> eqtn 1
1.00 = (52 – m) / s --> eqtn 2
Rewriting eqtn 1 in terms of m:
0.5 s = 45 – m
m = 45 – 0.5 s -->
eqtn 3
Rewriting eqtn 2 in terms of m:
1.00 s = 52 – m
m = 52 – 1.00 s -->
eqtn 4
Equating eqtn 3 and 4:
45 – 0.5 s = 52 – 1.00 s
0.5 s = 7
s = 14
From eqtn 4:
m = 52 - 1.00 * 14
m = 38
Therefore answers are:
m = 38 and s = 14
