Lucas calls his girlfriend Margaret every day on his cell phone. The time X, in hours, that they talk in a day is uniformly distributed between 0 and 2. Lucas pays $2 per hour that he is on the phone, plus a flat rate of $5 per day. So Y = 2X + 5 is the size of his bill per day.
a. Find the probability that he spends more than $6 on a given day for his cell phone service.
b. Find the expected amount that he spends on a given day for his cell phone service.
c. Find the standard deviation of the amount that he spends on a given day for his cell phone service.