0 like 0 dislike
42 views
List the basic properties of the normal distribution
| 42 views

0 like 0 dislike

Basic Properties of the Normal Distribution

The normal distribution, also known as the Gaussian distribution, has several key properties:

Symmetry: The distribution is symmetric about its mean, $$\mu$$, meaning the left side is a mirror image of the right side.

Mean, Median, and Mode: For a normal distribution, the mean, median, and mode are all equal and located at the center.

Bell-shaped Curve: It has a bell shape with the peak at the mean, $$\mu$$, and it approaches the x-axis asymptotically.

Defined by Two Parameters: Its shape is determined by the mean ($$\mu$$) and standard deviation ($$\sigma$$), where $$\mu$$ affects the location and $$\sigma$$ the spread.

Area under the Curve: The total area under the curve equals 1, a property of all probability distributions.

Empirical Rule: About 68\% of data falls within $$\pm 1\sigma$$, 95\% within $$\pm 2\sigma$$, and 99.7\% within $$\pm 3\sigma$$.

Percentiles: Percentiles can be calculated, which predict the probability of a variable falling within certain ranges.

Inflection Points: There are inflection points at $$\mu - \sigma$$ and $$\mu + \sigma$$, where the graph's curvature changes.

Asymptotic: The tails of the curve are asymptotic to the x-axis, meaning they get closer indefinitely but never touch it.

Standard Normal Distribution: A special case with $$\mu = 0$$ and $$\sigma = 1$$, where any normal distribution can be standardized using the z-score formula.

by Platinum (109k points)

0 like 0 dislike
2 like 0 dislike
0 like 0 dislike
2 like 0 dislike
0 like 0 dislike
0 like 0 dislike
3 like 0 dislike
2 like 0 dislike
1 like 0 dislike
0 like 0 dislike
0 like 0 dislike
2 like 0 dislike
1 like 0 dislike
2 like 0 dislike