The standard deviation of the normal distribution is a measure of how spread out the distribution is from its mean. It is the square root of the variance of the distribution. Here are some key points about standard deviation:

- The standard deviation can be represented with the Greek letter sigma (σ).
- A normal distribution with a small standard deviation will have most of its data points close to the mean, while a distribution with a large standard deviation will have data points that are more spread out.
- About 68% of the data in a normal distribution falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
- The standard deviation can be used to calculate confidence intervals, or ranges of values that are likely to contain the population parameter being estimated.
- The standard deviation is influenced by outliers in the data, so it may not be the most appropriate measure of dispersion in skewed or non-normal distributions.

Overall, the standard deviation is a useful measure of how tightly or loosely clustered data is around the mean in a normal distribution, and can be used to make inferences about the population based on sampled data.

## Example problem for standard deviation of normal distribution

What is the formula for standard deviation of normal distribution?

- The formula for standard deviation of normal distribution is:
- σ = √( Σ(xi – μ)^2 / N )

What does standard deviation of normal distribution represent?

- Standard deviation of normal distribution represents the amount of variation or dispersion of a set of data from the mean.

How does the standard deviation affect the normal distribution curve?

- A smaller standard deviation will result in a narrower and taller normal distribution curve, while a larger standard deviation will result in a flatter and wider normal distribution curve.

What is the relationship between standard deviation and the empirical rule?

- The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.