Summarizing Data using Z-Scores: The Standard Normal Distribution

Flashcards derived from lecture notes on Z-scores and Normal Distribution, covering key definitions and concepts.

Standard Normal Distribution

A normal distribution with a mean of 0 and a standard deviation of 1, denoted as N(0,1).

Z-Score

A standard score that indicates how many standard deviations a data point is from the mean.

Probabilities

The likelihood that some event will occur, expressed as percentages or proportions.

Normal Distribution

A symmetric, unimodal distribution often depicted as bell-shaped with limits extending to +/- infinity.

Area under the distribution

The total area under the curve of a probability distribution, which equals 100% or 1.0.

Transformation to Z-Scores

The process of converting raw scores into z-scores to analyze data in terms of standard deviations from the mean.

Z-Table

A table used to find the area under the curve for z-scores in a standard normal distribution.

Percentile

The value below which a given percentage of observations in a group of observations falls.

Type 1 Z-Score Problem

Calculating the area under the curve given a raw score.

Type 2 Z-Score Problem

Finding a raw score given the area under the curve.

Symmetry of Normal Distribution

The areas for positive z-scores above the mean and negative z-scores below the mean are equal.

Mean (µ)

The arithmetic average of a set of values, central to the normal distribution.

Standard Deviation (σ)

A measure that quantifies the amount of variation or dispersion in a set of data values.

Percentile Rank

A measure that indicates the value below which a given percentage of observations fall.

Raw Score

The original value from a dataset before any standardization or transformation.

Bell-shaped Curve

Visual representation of a normal distribution, symmetric about the mean.