If Jonathan got a T-score of 30 in a personality test, what is his z-score?a.-3b.-1c.-4d.-2

To find Jonathan's z-score from his T-score of 30, we will follow these steps:

1. ### Break Down the Problem

We need to convert the T-score into a z-score. The conversion formula between T-scores and z-scores is as follows: $Z = \frac{(T - 50)}{10}$ where $T$ is the T-score.

2. ### Relevant Concepts

• T-score is a standardized score that shifts the mean to 50 and standard deviation to 10.
• Z-score is another form of standardization, expressing how many standard deviations an element is from the mean.

3. ### Analysis and Detail

Substituting Jonathan's T-score into the formula: $Z = \frac{(30 - 50)}{10}$

Calculating the numerator: $30 - 50 = -20$

Now, dividing by the standard deviation: $Z = \frac{-20}{10} = -2$

4. ### Verify and Summarize

The calculations show that converting a T-score of 30 yields a z-score of -2. We can verify this by confirming the process and computations align with the conversion rules.

Final Answer

The z-score for Jonathan's T-score of 30 is $-2$. Thus, the correct answer is d. -2.