Final answer:
A normal distribution is a standard normal distribution if it has a mean of 0 and a standard deviation of 1. Z-scores are used to standardize values from any normal distribution to this standard normal framework.
Step-by-step explanation:
The standard normal distribution is a specific kind of normal distribution that has a mean (μ) of 0 and a standard deviation (σ) of 1. We know when a normal distribution is a standard normal distribution if these two conditions are met. Any normal distribution can be converted to a standard normal distribution by calculating the z-scores for its data points. A z-score represents the number of standard deviations a data point is from the mean of the distribution. When the mean is zero and the standard deviation is one, the z-scores correspond to the actual values of the dataset, and we're working with a standard normal distribution.
To calculate a z-score, use the formula z = (x - μ) / σ, where x is a value in the dataset, μ is the mean, and σ is the standard deviation of the original normal distribution. The z-score translates a value from any normal distribution to a standardized value that can be understood in the context of the standard normal distribution.