a.A normal distribution is any distribution that is not unusual

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I would suggest a more specific definition for a normal distribution. It occurs solely by chance. Does that fit your definition of "not unusual"?

To determine if a distribution is normal or not, we need to assess its shape. A normal distribution, also known as a Gaussian distribution, has a characteristic bell-shaped curve, with the majority of data clustered around the mean, while increasingly fewer data points are found farther away from the mean. This shape is symmetric, meaning that the curve is mirrored on either side of the center.

To determine if a distribution is normal or not, there are a few methods you can use:

1. Visual inspection: Plot the data on a histogram or a density plot. If the data forms a bell-shaped curve, it is likely to be normally distributed. However, keep in mind that this method is subjective and may not be reliable, especially with small sample sizes.

2. Quantile-Quantile (Q-Q) plot: A Q-Q plot compares the observed distribution to the expected distribution of a normal distribution. If the data points fall approximately along a straight line, it indicates that the data follows a normal distribution.

3. Statistical tests: There are several statistical tests available to formally test for normality. The most commonly used ones are the Shapiro-Wilk test and the Kolmogorov-Smirnov test. These tests assess whether the observed data significantly deviates from a normal distribution.

However, it's important to note that the term "normal distribution" is often used more broadly to refer to any distribution that is not unusual or skewed. In this broader context, a normal distribution implies a symmetric distribution with the majority of data points around the mean.