Adding two independent normal random variables

Hi guys,

I couldn't figure this one out:

Bulbs fail with normal distribution: mean = 400 days, st. dev = 100 days.

Bulbs are replaced every 365 days. What is the probability that a bulb and its replacement will fail in that period?

There's a hint though: The sum of two iid normal random variables is ______

The book also says this: The sum of independent random variables whose distributions are normal is a random variable having the normal distrbution.

I cant figure out neither the excerpt, the hint, nor the answer. Can someone please explain what it means?