Answer :
All of the following properties are indeed associated with Student's t-distributions: satisfies the 68-95-99.7 Rule, symmetric, unimodal, and bell-shaped.
Student's t-distributions have several characteristics that make them useful in statistical inference. They are symmetric, meaning that the distribution is the same on both sides of the mean. They are also unimodal, which means they have a single peak or mode. Additionally, they are bell-shaped, resembling a symmetrical, bell-shaped curve.
Student's t-distributions do not satisfy the property that "Area Under the Curve is One." Unlike some other probability distributions, such as the normal distribution, the total area under the curve of a t-distribution is not equal to one. The area under the curve represents the probability, and for a t-distribution, the total probability is not necessarily equal to one.
While Student's t-distributions possess the properties of the 68-95-99.7 Rule, symmetry, unimodality, and bell-shape, they do not adhere to the property that the "Area Under the Curve is One." It is important to understand these characteristics when using t-distributions in statistical analysis and hypothesis testing.
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