Density Curves and Normal Distribution

These flashcards cover the key vocabulary and concepts related to density curves and the normal distribution as discussed in the lecture notes.

Density Curve

A density curve is a curve that is always on or above the horizontal axis and has an area of exactly 1 underneath it.

Median of a Density Curve

The median of a density curve is the equal-areas point that divides the area under the curve in half.

Mean of a Density Curve

The mean of a density curve is the balance point, where the curve would balance if made of solid material.

Normal Distribution

A distribution with a bell-shaped density curve, parameterized by mean (μ) and standard deviation (σ).

Empirical Rule

Approximately 68% of observations fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Z-Score

A standardized value calculated as z = (x - μ) / σ, representing how many standard deviations an observation is from the mean.

Standard Normal Distribution

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

Area Under the Normal Curve

Represents proportions (probabilities) of observations from the normal distribution.

TI-83TM Calculator

A calculator used to compute areas under the normal curve; commands include normalcdf for finding areas.

Cumulative Proportion

The area under the curve to the left of a number x, representing the proportion of observations below that value.

Inverse Normal Calculations

Finding a value x corresponding to a given area proportion under the normal curve using the equation: x = μ + σz.