A store sells batteries and claims that their life time is 250 hours. Let us assume that the probability distribution of each batterie's life time obeys a (continuous) uniform distribution between 100 and 350 hours. Assuming we take out a new battery..

1) What is the probability that the life time of this battery is at least 200hours?

2) What is the probability that the life time of this battery is between 200 and 400 hours?

3) A customer purchases two new batteries. (each battery is independent)

. i. What is the expected combined life time of the two batteries

ii. What is the variance of the combined life times of the batteries?

Solve without using calculus