Density Curves and Normal Distribution

These flashcards cover key terms and concepts related to density curves and normal distribution, aiding in the understanding of probability and statistical modeling.

Density Curve

A smooth curve that fits on a histogram, used to represent continuous random variables.

Normal Distribution

A probability distribution that is symmetric, unimodal, and bell-shaped, commonly used to model real-valued random variables.

P(a<x<b)

The probability that a random variable x falls within the interval (a, b), represented by the area under the density curve between a and b.

Z-score

A standardized value representing the number of standard deviations a data point is from the mean.

Empirical Rule (68-95-99.7 Rule)

Describes the percentage of observations within one, two, and three standard deviations from the mean in a normal distribution.

Nearly Normal Condition

The requirement that the shape of data’s distribution is unimodal and symmetric to assume normality in the model.

Normal Probability Plot

A graphical display that helps assess if the data follows a normal distribution; a roughly straight line indicates normality.

Continuous Random Variables

Variables that can take any value within a specified range, typically described using density curves.