Normal probability question help

Hello Statisticians!

I would really really appreciate any help with this question:

Q. The grade a student receives in an exam is given my a normal distribution with mean 3.5 and variance 1/16.
1. Find the probability the the student scores between 3.4 and 3.6 for an individual course.
2. What is the probability that the average score for 36 courses, all following a normal distribution, will be between 3.4 and 3.6?

I found the answer to part 1. to be 0.3108, which is the same as given in the textbook.
However, I do not know how to work out part 2. I would really appreciate if somebody could please explain the exact way to solve such questions. The correct answer given in the textbook is 0.9836.

Thank you in advance. xx