Chapter 6: Normal Distributions and Central Limit Theorem Vocabulary

Flashcards defining key statistical vocabulary terms from Chapter 6, including normal distributions, z-scores, skewness metrics, and the Central Limit Theorem.

Continuous Random Variable

A variable that can assume all values in the interval between any two given values.

Empirical Rule

A rule stating that for a bell-shaped or normal distribution, approximately 68% of data values fall within 1 standard deviation of the mean, 95% fall within 2 standard deviations, and approximately 100% (or 99.7%) fall within 3 standard deviations.

Standard Score (z-score)

A value obtained by subtracting the mean from an observed value and dividing the result by the standard deviation, calculated as $z = \frac{X - \mu}{\sigma}$.

Normal Distribution

A continuous, bell-shaped, and symmetric probability distribution for a random variable, denoted as $X \sim N(\mu, \sigma^2)$

Standard Normal Distribution

A specific normal distribution with a mean equal to 0 and a standard deviation equal to 1, denoted as $Z \sim N(0, 1)$

Decibel

A measure of the intensity of sound.

Pearson Coefficient (PC)

An index used to check for skewness in a dataset, calculated as $PC = \frac{3(\bar{x} - \text{median})}{s}$. A value where $PC \ge 1$ or $PC \le -1$ indicates significantly skewed data.

Sampling Distribution of Sample Means

A distribution formed by using the means computed from all possible random samples of a specific size taken from a population.

Sampling Error

The difference between the sample measure and the corresponding population measure due to the fact that the sample is not a perfect representation of the population.

Central Limit Theorem (CLT)

A theorem stating that as sample size $n$ increases without limit, the shape of the distribution of sample means taken with replacement will approach a normal distribution, applicable when $n \ge 30$.

Unbiased Estimator

A sample statistic whose expected value equals the population parameter that it is estimating, such as $E(\bar{X}) = \mu$.