Question

a population of scores with μ=73 and σ=6 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: 67,70,79,82

Answer 1

We have to find the z scores for each value using the previous data and then using that z score with new data to find new score

For 67

z score = (x-mean)/sd

= (67-73)/6

= -1

New score calculation

X = mean + z*sd

= 50 + (-1*10)

= 40

For 70

z score = (x-mean)/sd

= (70-73)/6

= -0.5

New score calculation

X = mean + z*sd

= 50 + (-0.5*10)

= 45

For 79

z score = (x-mean)/sd

= (79-73)/6

= 1

New score calculation

X = mean + z*sd

= 50 + (1*10)

= 60

For 82

z score = (x-mean)/sd

= (80-73)/6

= 1.5

New score calculation

X = mean + z*sd

= 50 + (1.5*10)

= 65

So, new values are 40,45,60,65