# 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:

Number of Degrees of Freedom (\(df\))
Two-Tailed:
≤ X ≤
Left-Tailed:
X ≤
Right-Tailed:
X ≥

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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