**5.** A measurement *x* in a sample with mean 2.3 and standard deviation 1.3 has a *z*-score equal to -2.

What is *x*?

[A] -0.3 [B] 4.6 [C] 4.9 [D] -2.6

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.*

A measurement x in a sample with mean 2.3 and standard deviation 1.3 has a z-score equal to -2. What is x? [A] -0.3 [B] 4.6 [C] 4.9 [D] -2.6

Learn how to calculate the value of x given a z-score of -2 in a sample with a mean of 2.3 and standard deviation of 1.3. This problem covers key statistical concepts, including z-scores, standard deviation, and mean. Suitable for students in Grades 9-12.

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