Please Help me solve the math in detail. Thank you.

The shelf life of a brand of alkaline battery (number of days it will remain functional after putting it on the shelf) normally distributed with a mean equal to 583 days and a standard deviation equal to 50 days (a) if the battery has been on the shelf for 630 days, what is the probability that it will function? (b) if the battery has been on the shelf for 430 days, what is the probability that it will not function? (c) if you want to be 90% sure that the battery will operate, how old a battery should you accept? [7]