# T-Distribution Probability Calculator

**Instructions:** Compute t-distribution probabilities using the form below. Please type the number of degrees of freedom associated to the t-distribution, and provide details about the event you want to compute the probability for:

More about the *t distribution probability*: The t-distribution is a type of continuous probability distribution that takes random values on the whole real line. The main properties of the t-distribution are:

- It is continuous (and as a consequence, the probability of getting any single, specific outcome is zero)
- It is "bell shaped", in the same way the normal curves are bell-shaped
- It is determined by one parameter: the number of degrees of freedom (df). For one sample, the number of degrees of freedom is df = n - 1, where n is the sample size
- It is symmetric with respect to 0
- The t-distribution "converges" to the standard normal distribution as the number of degrees of freedom (df) converges to infinity (+∞)

In order to compute probabilities associated to the t-distribution we can either use specialized software such as Excel, etc, or we can use t-distribution tables (normally available at college statistics textbooks. The use of the t-distribution arises when performing hypothesis testing (for the case when the population standard deviation is not known).

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