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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?

- $\mu=\mu_2; \sigma>\sigma_2$
- $\mu<\mu_2; \sigma>\sigma_2$
- $\mu>\mu_2; \sigma<\sigma_2$
- $\mu<\mu_2; \sigma=\sigma_2$