To solve for the value of x given that the z-score is -2, the mean is 2.3, and the standard deviation is 1.3, we can use the formula for the z-score:

$z = \frac{x - \mu}{\sigma}$

Where:

• $z$ is the z-score,
• $\mu$ is the mean,
• $\sigma$ is the standard deviation, and
• $x$ is the value we're solving for.

Plugging in the known values:

$-2 = \frac{x - 2.3}{1.3}$

Now, solve for $x$:

1. Multiply both sides by 1.3: $-2 \times 1.3 = x - 2.3$ $-2.6 = x - 2.3$

2. Add 2.3 to both sides: $x = -2.6 + 2.3$ $x = -0.3$

Thus, the value of x is $-0.3$, which corresponds to option [A] -0.3.

Would you like more details on z-scores or any further explanations?

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Here are 5 related questions to explore this topic further:

1. How would the z-score change if x was greater than the mean?
2. What does a z-score of 0 represent in a dataset?
3. How do you interpret positive and negative z-scores in terms of standard deviations?
4. How can z-scores be used to compare measurements from different datasets?
5. What is the relationship between the standard deviation and the spread of data?

Tip: A z-score represents how many standard deviations a data point is from the mean. A negative z-score indicates the point is below the mean.