For a sample of n = 100 scores, x = 45 corresponds to z = 0.50 and x = 52 corresponds to z = + 1.00. what are the values for the sample mean and standard deviation? m = 31 and s = 7 m = 31 and s = 14 m = 38 and s = 7 m = 38 and s = 14

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