Student's t-distribution is a sampling distribution for a random variable, t, derived from a normally distributed population, that is (1) single-peaked above the random variable's mean, median, and mode of zero, (2) perfectly symmetrical about this central value, and (3) characterized by tails extending indefinitely in both directions from the center, approaching, but never touching, the horizontal axis.

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Student's t-distribution has these characteristics: it is single-peaked and symmetrical around a mean of zero, with tails that extend indefinitely but never touch the horizontal axis, indicating the distribution of the t-statistic under the assumption of a normally distributed population.

Student's T-Distribution Is a Sampling Distribution for a Random Variable