Yes, the definition and formula shown in the image are correct.

Explanation:

The standard normal distribution is a special case of the normal distribution. It has:

• Mean ($\mu$) = 0
• Standard deviation ($\sigma$) = 1

If a random variable $x$ follows a normal distribution with any mean $\mu$ and standard deviation $\sigma$ (denoted as $N(\mu, \sigma)$), you can convert it into a standard normal distribution using the following transformation: $z = \frac{x - \mu}{\sigma}$ Where:

• $x$ is the original value,
• $\mu$ is the mean of the distribution,
• $\sigma$ is the standard deviation,
• $z$ is the standardized value, which will follow the standard normal distribution $N(0,1)$.

This is a key concept in statistics, especially for calculating probabilities and working with normal distributions.

Would you like more details on this topic or have any questions?

Here are 5 related questions to expand on this:

1. How do you calculate probabilities using the standard normal distribution?
2. What is the significance of the z-score in hypothesis testing?
3. How can we use the standard normal table to find areas under the curve?
4. What are common applications of the normal distribution in real life?
5. How do you convert a dataset to have a standard normal distribution?

Tip: When converting data to a standard normal form, it's called "standardization," which is essential in many statistical analyses, especially when comparing different datasets.