The normal daily human potassium requirement is in the range of 2000 to 6000 milligrams (mg), with larger amounts required during hot summer weather. The amount of potassium in food varies, but bananas are often associated with high potassium, with approximately 422 mg in a medium-sized banana. Suppose the distribution of potassium in a banana is normally distributed, with mean equal to 422 mg and standard deviation equal to 13 mg per banana. You eat n = 3 bananas per day and T is the total number of milligrams of potassium you receive from them.
a. Find the mean and standard deviation of T.
b. Find the probability that your total daily intake of potassium from the three bananas will exceed 1300 mg.