Question

A population of scores with a μ = 43 a n d σ = 8 is standardized to create a new population distribution with a μ = 50 a n d σ = 10 . What is the new X value for each of the following scores from the original population?

a. X = 43

b. X = 47

c. X = 55

d. X = 35

Answer 1

When we standardize a population so as to change the value of μ and σ, the z-score of the X value remains unchanged in the old and new populations. We can use this fact to find the new X-value given an old X-value as follows:

which is the formula for calculating the new X-value from an old X-value.

a.

The new X-value corresponding to the old X-value of 43 is given by:

b.

The new X-value corresponding to the old X-value of 47 is given by:

c.

The new X-value corresponding to the old X-value of 55 is given by:

d.

The new X-value corresponding to the old X-value of 35 is given by:

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