The distribution of marks scored by a large class in an exam can be represented as a normal distribution with mean $\mu$ and standard deviation $\sigma$. In a follow-up exam in the same class, everyone scored $5$ marks more than their respective score in the earlier exam. For this follow-up exam, the distribution of marks can be represented as normal distribution with mean $\mu_2$ and standard deviation $\sigma_2$. Which one of the following is correct?

1. $\mu=\mu_2; \sigma>\sigma_2$
2. $\mu<\mu_2; \sigma>\sigma_2$
3. $\mu>\mu_2; \sigma<\sigma_2$
4. $\mu<\mu_2; \sigma=\sigma_2$