The machinery at a food-packing plant is able to put exactly 12 ounces of juice in every bottle. However, some items such as apples come in variable sizes so it is almost impossible to get exactly 3 pounds of apples in a bag labeled "3 lbs." Therefore, the machinery is set to put an average of μ = 50 ounces (3 pounds and 2 ounces) in each bag. The distribution of bag weights is approximately normal with a standard deviation of σ = 4 ounces.

a. What is the probability of randomly picking a bag of apples that weighs less than 48 ounces (3 pounds)?

b. What is the probability of randomly picking n = 4 bags of apples that have an average weight less than M = 48 ounces?