8 Questions
In a continuous probability distribution, what does the area under the curve represent?
Probability
What is the standard deviation of a normal distribution probability?
2
What is the z-score for a value that is one standard deviation below the mean in a standard normal distribution?
-1
What is the general form of the probability density function for a normal distribution?
$f(x) = \frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}$
What does the parameter $\mu$ represent in a normal distribution?
Mean, median, and mode
What is the variance of a normal distribution with standard deviation $\sigma$?
$\sigma^2$
What is a random variable with a Gaussian distribution called?
Normal deviate
Why are normal distributions important in statistics?
Due to the central limit theorem
Study Notes
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.
Test your knowledge of continuous probability with this quiz on normal distribution probability. Explore concepts such as standard deviation, the area under the curve, and z-scores in a standard normal distribution. Sharpen your understanding of these essential concepts in probability theory.
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