What differentiates Student's t-distribution from the standard normal distribution?

The distinguishing feature of Student's t-distribution compared to the standard normal distribution is that it has thicker tails, particularly for smaller sample sizes. This characteristic becomes more pronounced as the sample size decreases, which accounts for the increased uncertainty that arises when working with smaller data sets. The thicker tails of the t-distribution provide a more accurate estimation of the variability and potential for extreme values when the sample size is not large enough to justify the assumption of normality. As the sample size increases, the t-distribution approaches the standard normal distribution, ultimately becoming indistinguishable from it at larger sample sizes.

The other options do not correctly identify this unique property of the t-distribution. It does not have a mean greater than zero; rather, both it and the standard normal distribution have a mean of zero. The t-distribution can be used for any sample size, not just those greater than 30, although it becomes more reliable with larger samples. Lastly, a uniform distribution is fundamentally different from both the t-distribution and the standard normal distribution, which involve different characteristics related to probability density function shapes and tails.