Characteristics of Normal Distribution
Not what you're looking for?
The normal distribution has several characteristics that make it the underlying foundation of much of inferential statistical tools. List these characteristics and explain how they contribute to the power of the distribution as foundation of inferential decision making.
Purchase this Solution
Solution Summary
Why is the normal distribution important and why is it so commonly used?
Solution Preview
In probability theory and statistics, the normal distribution or Gaussian distribution is a continuous probability distribution that describes data that cluster around a mean or average. The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian function or bell curve.
Characteristics of Normal Distribution
1. The family of normal distributions is closed under linear transformations. That is, if X is normally distributed with mean μ and variance σ2, then a linear transform aX + b (for some real numbers a ≠ 0 and b) is also normally distributed.
2. Also if X1, X2 are two independent normal random variables, with means μ1, μ2 and standard deviations σ1, σ2, then their linear combination will also be normally distributed.
3. The converse of (1) is also true: if X1 and X2 are independent and their sum X1 + X2 is distributed normally, then both X1 and X2 ...
Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.