12. A model proposed for NBA basketball supposes that when two teams roughly the same record play each other, then the number of points sa in a quarter by the home, team minus the number scored by the visiting?

is approximately a normal random variable with mean 1.5 and variance 6.
In addition, the model supposes that the point differentials for the four quarters are independent. Assuming this model:

(a) What is the probability that the home team wins?

(b) What is the conditional probability that the home team wins given that it is behind by 5 points at halftime?

(c) What is the conditional probability that the home team wins given that it is ahead by 5 points at the end of the first quarter?