Random sample from Normal Distribution, why isn't the variance divided by n?

40 Views Asked by At

Below is a question containing parts b) and c). Further below is the mark scheme.

In part c) they take a random sample from T, which is normally distributed. I was expecting the distribution to change, so the variance is now divided by n. However, the mark scheme does not reflect this anywhere.

Why doesn't the answer to part c) reflect the variance being divide by n, given it is a random sample?

Question:

enter image description here

Mark scheme:

enter image description here