makes a distribution a normal distribution?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:**What makes a distribution a normal distribution?**
A normal distribution, often referred to as a bell curve, is a probability distribution that is symmetrical about the mean. This type of distribution shows that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, normal distribution will appear as a bell-shaped curve.
Key Characteristics of a Normal Distribution:
- **Symmetry**: It is symmetric around the mean.
- **Mean, Median, and Mode**: In a normal distribution, the mean, median, and mode of the data are the same.
- **Asymptotic Nature**: The tails of the distribution never actually touch the horizontal axis.
- **68-95-99.7 Rule**: About 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Understanding these features helps in identifying a dataset that follows a normal distribution, which is crucial for statistical analysis and inference.
Expert Solution
Step 1- Normal distribution
Properties of normal distribution
a) The mean , median and mode of a distribution is same it is normal.
b) The curve is symmetric at the center ( At the mean )
c) Exactly half values are to left of center and half values to the right of center most data lies around the average.
d) The total are under the curve is 1.
e) The logistic and t - distribution also have similar bell shape as normal distribution but ,the data is more distributed at extremes making tails heavier.
f) It is unimodal distribution (Only one peak) and shape is symmetric.
g) It has lesser difference from the mean making higher probability near mean and as it moves away the probability dimnishes.
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