Question

In a population distribution, a score of x= 28 corresponds to z= -1 and a score of X =34 corresponds to z= -0.50. Find the mean and standard deviation for the population

Answer 1

z = (X - mean)/sd
-1 = (28 - mean)/sd
mean - sd = 28 . . . (1)
-0.5 = (34 - mean)/sd
mean - 0.5sd = 34 . . . (2)

(1) - (2) => -0.5sd = -6
sd = -6/-0.5 = 12
From (1), mean = sd + 28 = 12 + 28 = 40

mean = 40
standard deviation = 12