Final answer:
The correct answer is 'a. lower; lower', indicating that with a larger number of degrees of freedom, the peaks and tails of the t-distribution become lower, resembling a standard normal distribution.
Step-by-step explanation:
The subject of the question pertains to the properties of the Student's t-distribution in relation to its degrees of freedom. As the degrees of freedom become larger, the t-curve becomes more like the standard normal distribution. This means that the peaks of the t-curve become lower and the tails become closer to the axis (i.e., less probability in the tails), which can be described as thinner tails.
The correct answer to the question is a. lower; lower.
It's important to note that as the degrees of freedom increase, the distribution approaches normality due to the Central Limit Theorem, which explains how the distribution of sample means approximates a normal distribution as the sample size becomes larger.