As the degrees of freedom increase, the t distribution approaches:

As the degrees of freedom increase, the t distribution approaches a normal distribution due to its characteristics and the Central Limit Theorem. The t distribution is used primarily when the sample size is small and/or the population standard deviation is unknown. It is wider and has heavier tails than the normal distribution, reflecting the increased variability associated with smaller sample sizes.

As the sample size—and consequently the degrees of freedom—increases, the sample mean's distribution becomes more normally distributed due to the Central Limit Theorem. This means that with larger sample sizes, the distinctions between the t distribution and the normal distribution diminish, leading the t distribution to converge toward the normal distribution.

This convergence is an essential concept in statistics, particularly in hypothesis testing and constructing confidence intervals for means. The normal distribution is a key reference point because many statistical methods are based on the assumption of normality, which justifies the use of the normal distribution as the sample size increases.