Mean, Median, and Mode: A distinctive trait of a normal distribution is the convergence of the mean, median, and mode. In essence, these central measures of a dataset align, illustrating the uniform nature of the distribution.

Bell-Shaped Curve: A salient feature of a normal distribution is its bell-shaped curve, gradually diminishing towards the tails. The majority of observations are huddled around the mean, underscoring the central tendency of the data.

Empirical Rule: Approximately 68% of observations fall within a single standard deviation from the mean, while 95% are enveloped within two standard deviations, and 99.7% lie within the boundary of three standard deviations.

Statistical Inference: The normal distribution finds widespread application in statistical inference. Given its beneficial properties and the ubiquity of normally distributed data in real-world scenarios, it becomes instrumental in hypothesis testing, confidence interval estimation, and regression analysis.

Standard Normal Distribution: A variant of the normal distribution, the standard normal distribution, harbors a mean of 0 and a standard deviation of 1. This distribution facilitates the creation of Z-scores, which standardize data, enabling meaningful comparisons across different datasets or variables.

Not Suitable for All Data: A normal distribution does not apply to all data. Certain datasets may exhibit skewed or non-symmetric distributions, necessitating alternative analysis methods.

Inappropriate for Discrete Data: As a continuous distribution, the normal distribution is inappropriate for modeling discrete data, encompassing counts or categorical variables.

Sensitive to Outliers: The mean and standard deviation, responsible for determining the shape of a normal distribution, are susceptible to outliers, potentially leading to erroneous conclusions if the data contains extreme values.

Incarceration rates vary greatly worldwide, with some countries reflecting high-prisoner populations due to strict legal systems while others maintain low conviction rates due to lenient laws or underreporting.

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