Student's distribution says that . As the sample size increases (i.e. ), , i.e. the sample variance converges to the population variance by the law of large numbers. By Slutsky's theorem (which roughly just says that we can "plug" this convergence into the previous one), it follows that: What follows as a consequence? The student's t-distribution converges to the normal distribution as increases The normal distribution converges to the student's t-distribution