Which of the following statements is true?
I. The area under the $t$-distribution curve to the right of a positive $t$ value with $6$ degrees of freedom is larger than the area to the right of the same t value with $18$ degrees of freedom.
II. The higher the degrees of freedom, the closer the $t$-distribution is to the standard normal distribution.
III. The $t$-distribution is appropriate to use when the population standard deviation is known.