Suppose the data value, x, is normally distributed with a mean of 44 and a standard deviation of 1.
What is the z score of x = 40?
If necessary round to the nearest tenth.

To find the z-score of a value in a normal distribution, we use the following formula:

\[
z = \frac{x - \mu}{\sigma}
\]

Where:
- \( z \) is the z-score,
- \( x \) is the data value,
- \( \mu \) is the mean, and
- \( \sigma \) is the standard deviation.

Given:
- \( x = 40 \),
- \( \mu = 44 \),
- \( \sigma = 1 \).

Now, substitute the values into the formula:

\[
z = \frac{40 - 44}{1} = \frac{-4}{1} = -4
\]

So, the z-score of \( x = 40 \) is \( -4 \).

### Would you like to know more details or have any questions?

Here are 5 related questions:
1. What does a z-score represent in a normal distribution?
2. How can you interpret a negative z-score?
3. How do you calculate probabilities using z-scores?
4. What is the probability of a z-score of -4 in a standard normal distribution?
5. How does changing the standard deviation affect the z-score?

**Tip**: A z-score tells you how many standard deviations a data point is from the mean.

Suppose the data value, x, is normally distributed with a mean of 44 and a standard deviation of 1. What is the z score of x = 40? If necessary round to the nearest tenth.

Learn how to calculate the z-score of a data value, x = 40, in a normal distribution with a mean of 44 and a standard deviation of 1. This problem covers key statistical concepts like z-scores and normal distribution. Suitable for students in Grades 10-12.

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