A discrete random variable $X$ takes values from $1$ to $5$ with probabilities as shown in the table. A student calculates the mean of $X$ as $3.5$ and her teacher calculates the variance of $X$ as $1.5$. Which of the following statements is true?
$$\begin{array}{|c|c|c|c|c|c|}
\hline \text{k} & 1 & 2 & 3 & 4 & 5 \\
\hline \text{P(X=k)} & 0.1 & 0.2 & 0.4 & 0.2 & 0.1 \\
\hline \end{array}$$
- Both the student and the teacher are right
- Both the student and the teacher are wrong
- The student is wrong but the teacher is right
- The student is right but the teacher is wrong