Normal distribution

What is a Random Variable?

A variable whose values are determined by chance, such as the result of a rolled dice.

Define Probability Distribution.

A mathematical function that describes how the probabilities of a random variable are distributed across its possible values.

What are the two types of probability distributions?

Discrete: Random variables with a countable/finite set of outcomes (e.g., Binomial distribution).

• ​Continuous: Random variables with an uncountable/infinite set of outcomes (e.g., Normal distribution).

What are the three primary characteristics of a Normal Distribution?

It is continuous, symmetric, and bell-shaped. It is also known as the Gaussian distribution.

Where are the Mean, Median, and Mode located in a normal distribution?

They are all equal and located at the exact center of the distribution.

What factors determine the shape and position of a normal distribution curve?

The mean (\mu) and the standard deviation (\sigma).

What is the total Area Under the Curve (AUC) for a normal distribution?

The total area is 1. In a standard normal distribution, this area represents the probability.

What defines a Standard Normal Distribution?

A normal distribution with a mean of 0 and a standard deviation of 1.

What is a Z-score (or Z-value)?

The number of standard deviations a particular value (X) is away from the mean.

How do you find the area to the right of a Z-value?

Look up the Z-value in the distribution table and subtract that area from 1.

State the Central Limit Theorem.

As sample size (n) increases without limit, the shape of the distribution of sample means will approach a normal distribution, regardless of the population's original shape

What is Sampling Error?

The difference between a sample measure and the actual population measure

What are the Reference Ranges (Empirical Rule) for a normal curve?

Within 1 SD: ~68% of the area.

​Within 2 SD: ~95% of the area.

​Within 3 SD: ~99.7% of the area.