A distribution with μ=65 and σ=6 is being standardized to produce a new mean of μ=50 and a new standard deviation of σ=10. Find the new standardized value for each of the following scores from the original distribution: 71, 62, 74, and 53.

Answer 1

Step 1:
The z-score for each score can be calculated using:
z = (x – μ) / σ
For the first score given, 71:
z = (71 – 65) / 6
z = 6/6
z = 1
This means that the score 71 is 1 standard deviation above the mean.

Step2:
Use the formula again to figure out what the equivalent score would be in the new grading system of mean 50 and standard deviation 10:
z = (x – μ) / σ
1 = (x - 50) / 10
10 = x - 50
x = 60
So the original score of 71 would be equivalent to a score of 60 in the new system.

Repeat steps 1 and 2 for each of the remaining three scores.