Question

A population of scores with µ = 73 and σ = 20 is standardized to create a new population with µ = 50 and σ = 10. What is the new value for each of the following scores from the original population?    Scores: 33, 65, and 77.

Answer 1

Solution:
Given in the question
Original Population mean (o) = 73
Original Population standard deviation (o) = 20
So Z-score for number X = 33 can be calculated as
Z = (X-o)/0 = (33-73)/20 = -2
Z-score at X = 65 is
Z= (65-73)/20 = -0.4
Z-score at X = 77
Z-score = (77-73)/20 = 0.2
Now New population mean and standard deviation can be calculated as
New Mean (n) = 50
New standard deviation (n) = 10
So at Z=-2, X value can be calculated as
X = n + Z-score * n = 50 - 2*10 = 30
At Z = -0.4, X value is
X = 50 - 0.4*10 = 50-4 = 46
At Z= 0.2, X value is
X = 50 + 0.2*10 = 52
So New scores a re 30, 46 and 52 for each of the following scores from the original population i.e. 33,65 and 77 respectively.