A score that is 2 points higher than the sample mean has a z-score of z = 0.50,and a score of X = 44 has a z-score of -1.00.What is the sample mean?
A)M = 40
B)M = 46
C)M = 48
D)M = 50

Question

Quizplus · Accepted Answer

Using the formula: 
z = (X - M) / SD

We can set up two equations and solve for two unknowns (M and SD).

z1 = 0.5, X1 = M + 2, 
0.5 = (M + 2 - M) / SD 
0.5SD = 2 
SD = 4

z2 = -1, X2 = 44 
-1 = (44 - M) / 4 
-4 = 44 - M 
M = 48

Therefore, the sample mean is M = 48, which is choice C.

A Score That Is 2 Points Higher Than the Sample