Probability Distributions: The Normal Distribution

A collection of vocabulary flashcards based on the lecture notes on probability distributions, particularly focusing on the normal distribution and related statistical concepts.

Normal Distribution

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Standard Deviation (SD)

A measure of the amount of variation or dispersion of a set of values.

Central Limit Theorem

The theorem that states that the sampling distribution of the sample mean will approximate a normal distribution as the sample size becomes larger, regardless of the distribution of the population.

Sampling Variability

The variation in sample statistics that occurs by chance because the sample represents only a subset of the population.

Confidence Interval (CI)

A range of values that is likely to contain the population parameter with a certain level of confidence.

Z-value

A measure of how many standard deviations an element is from the mean.

Sampling Distribution

The distribution of all possible values of a statistic (like the sample mean) from all possible samples drawn from a population.

Chi-squared Test

A statistical test used to determine if there is a significant difference between the expected and observed frequencies in a contingency table.

Type 1 Error

Rejecting the null hypothesis when it is actually true.

Type 2 Error

Failing to reject the null hypothesis when it is actually false.

Probability Density Function (pdf)

A function that describes the likelihood of a continuous random variable taking on a particular value.

Bell Curve

Another name for the normal distribution, representing a graphical depiction of the probability distribution.

Proportion

A part or portion of a whole, often expressed as a fraction or percentage.

Empirical Rule

A rule stating that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, about 95% within two, and about 99.7% within three.