Question

It is assumed that the lifetime of a light bulb attached to the entrance of a home follows a normal distribution N(180,100). When it is replaced on New Year day, what is the probability that it have to be replaced more than once (≧2) in the year?

(The answer should be rounded to the third decimal place and answer to the second decimal place such as 0.12.)
Hint 1:
Let X be the lifetime of the first light bulb, and Y be the lifetime of the second light bulb, then X and Y are independent.
What we want is the probability of the event X+Y < 365.
Hint 2:
When X and Y follow the normal distributions, X+Y also follow the normal distribution.

Answer 1