https://file.aiquickdraw.com/mathbot/file/1729834939346qg0r0bkv.jpg

The problem in the image asks to find the data value corresponding to a **z-score** of -3.94 in a normal distribution with a mean (μ) of 64.2 and a standard deviation (σ) of 2.53.

We use the formula for converting a z-score to a data value (x):
\[
x = \mu + z \cdot \sigma
\]

Where:
- \( \mu = 64.2 \)
- \( \sigma = 2.53 \)
- \( z = -3.94 \)

Now, let's calculate the data value:
\[
x = 64.2 + (-3.94) \cdot 2.53
\]
\[
x = 64.2 - 9.9722
\]
\[
x = 54.2 \ (rounded \ to \ the \ nearest \ tenth)
\]

So, the data value is approximately **54.2**.

Would you like more details on how this was calculated or have any questions? 

Here are 5 related questions for further practice:
1. How would the data value change if the z-score were -2.5 instead?
2. Can you explain what a z-score of 0 would mean in this context?
3. How does changing the standard deviation affect the data value for a fixed z-score?
4. How would you interpret a positive z-score using this formula?
5. What is the probability associated with a z-score of -3.94?

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

A normal distribution has mean 64.2 and standard deviation 2.53. Find the data value corresponding to z = -3.94.

Learn how to calculate the data value corresponding to a z-score of -3.94 in a normal distribution with a mean of 64.2 and a standard deviation of 2.53. This problem covers key concepts such as the z-score formula and normal distribution.

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