Student's $t$ distributions are symmetric about a value of $t$. What is that value?

• A. $t=1$
• B. $t=0$
• C. $t=2$
• D. $t=-1$

Answer: (B)

Verified step by step guidance

1. Recall that the Student's t-distribution is a continuous probability distribution that is symmetric and bell-shaped, similar to the normal distribution but with heavier tails.
2. Understand that the symmetry of the distribution means it is centered around a specific value, which is also the mean, median, and mode of the distribution.
3. Identify that for the Student's t-distribution, this central value is zero, meaning the distribution is symmetric about \(t = 0\).
4. Recognize that this property holds regardless of the degrees of freedom parameter in the t-distribution.
5. Therefore, the value about which the Student's t-distribution is symmetric is \(t = 0\).