Answer :
All of the following properties are true for (Student) t-distributions: satisfies 68-95-99.7 Rule, symmetric, unimodal, and bell-shaped. Therefore, none of them is not a property of (Student) t-distributions.
1. Satisfies 68-95-99.7 Rule: This property states that in a (Student) t-distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. This rule is also applicable to the (Student) t-distributions, just like the normal distribution.
2. Symmetric: (Student) t-distributions are symmetric, meaning that the distribution is equally balanced on both sides of the mean. This symmetry allows for the calculation of probabilities and critical values in a straightforward manner.
3. Unimodal: A (Student) t-distribution has a single peak, making it unimodal. The shape of the distribution is characterized by one central peak and gradually decreasing values as we move away from the mean.
4. Bell-shaped: Similar to the normal distribution, (Student) t-distributions are bell-shaped. This means that the majority of the data is concentrated around the mean, with the frequency of values decreasing as we move towards the tails.
5. Area Under the Curve is One: This property holds true for all probability distributions, including (Student) t-distributions. The total area under the curve represents the probability of all possible outcomes and is always equal to one. Therefore, all of the listed properties are valid for (Student) t-distributions, and none of them is not a property of these distributions.
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