Normal Distribution Probability Quiz

Continuous Probability Distribution

• The area under the curve represents the probability of a continuous random variable taking on a value within a certain range.

Standard Normal Distribution

• The standard deviation of a standard normal distribution is equal to 1.
• The mean of a standard normal distribution is equal to 0.

Z-Score

• A z-score of -1 represents a value that is one standard deviation below the mean in a standard normal distribution.

Normal Distribution

• The general form of the probability density function for a normal distribution is $f(x) = \dfrac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$.
• The parameter $\mu$ represents the mean of the normal distribution.
• The variance of a normal distribution with standard deviation $\sigma$ is equal to $\sigma^2$.

Gaussian Distribution

• A random variable with a Gaussian distribution is called a normal random variable.

Importance of Normal Distributions

• Normal distributions are important in statistics because they are used to model real-valued random variables that are assumed to be symmetric around the mean and have a continuous range.