Explanation:
The distribution that is symmetrical around t = 0 is known as the t-distribution.

T-Distribution:
The t-distribution is a probability distribution that is used to estimate population parameters when the sample size is small or when the population standard deviation is unknown. It is similar to the normal distribution but has heavier tails.

Characteristics of the t-distribution:
1. The t-distribution is centered around t = 0.
2. The shape of the t-distribution is bell-shaped and symmetrical.
3. The t-distribution has a mean of 0.
4. The t-distribution has a parameter called degrees of freedom (df), which affects the shape of the distribution. As the degrees of freedom increase, the t-distribution becomes closer to the standard normal distribution.

Why t-distribution is symmetrical around t = 0:
The t-distribution is symmetrical around t = 0 because the formula for calculating the t-value takes into account the difference between the sample mean and the population mean. When the sample mean is equal to the population mean (i.e., the difference is 0), the t-value is 0. As the difference between the sample mean and the population mean increases, the t-value moves further away from 0 in either the positive or negative direction.

Other Distributions:
- Normal Distribution: The normal distribution is also symmetrical, but it is not centered around t = 0. The normal distribution has a mean and standard deviation that determine its shape and location.
- Poisson Distribution: The Poisson distribution is not symmetrical. It is used to model the number of events that occur in a fixed interval of time or space.
- Binomial Distribution: The binomial distribution is not symmetrical. It is used to model the number of successes in a fixed number of independent Bernoulli trials.

Conclusion:
In conclusion, the distribution that is symmetrical around t = 0 is the t-distribution. This distribution is used when the sample size is small or when the population standard deviation is unknown. The t-distribution is centered around t = 0 and has a bell-shaped and symmetrical distribution.