Question

Given that the mean number of secondary reinforcements each day in a psychiatric hospital token economy is 10 tokens and the standard deviation is 4.5 tokens, convert the following to z scores. A. 16 tokens B. 19 tokens C. 8 tokens D. 9 tokens E 10 tokens F. 7 tokens

Answer 1

The z-scores for the given values are:

A. 1.33

B. 2

C. -0.44

D. -0.22

E. 0

F. -0.67

Explanation:

To convert a given value to a z-score, we can use the formula:

z = (x - μ) / σ

Where:

z is the z-score

x is the given value

μ is the mean

σ is the standard deviation

In this case, the mean (μ) is 10 tokens and the standard deviation (σ) is 4.5 tokens.

Let's calculate the z-scores for the given values:

A. 16 tokens:

z = (16 - 10) / 4.5

z = 6 / 4.5

z ≈ 1.33

B. 19 tokens:

z = (19 - 10) / 4.5

z = 9 / 4.5

z = 2

C. 8 tokens:

z = (8 - 10) / 4.5

z = -2 / 4.5

z ≈ -0.44

D. 9 tokens:

z = (9 - 10) / 4.5

z = -1 / 4.5

z ≈ -0.22

E. 10 tokens:

z = (10 - 10) / 4.5

z = 0 / 4.5

z = 0

F. 7 tokens:

z = (7 - 10) / 4.5

z = -3 / 4.5

z ≈ -0.67

Therefore,

A. 1.33

B. 2

C. -0.44

D. -0.22

E. 0

F. -0.67