For each of the following parts, answer what is being asked and show your work. If you are asked to find a value of Y, find it to 3 decimal places. If you were asked to find a probability, find it to 4-decimal places using the z-table. You are not required to draw the normal distribution, although it may help you get the right answer. (Show your work!) Suppose that the makers of a new longer lasting battery for its most popular cellphone claims that it will last 12 hours, on average, before it needs recharging with a standard deviation of 0.5 hours,

a) what is the probability that, a newly recharged battery, will last at least 12.5 hours before it needs recharging? b) What is the probability that a newly recharged battery will last no more than 10.8 before it needs recharging? c) What is the time that is exceeded 10% of the time before the battery needs recharging?