A machine is designed to fill some snack-sized potato chips with normally distributed weights with a mean of 6 oz. and standard deviation of 0.5 oz. If one bag of potato chips is randomly selected,
a. What is the probability that its weight is between 2.5 oz to 7.5 oz?
b. What is the probability that its weight is less than 7.5 oz?
c. If 40 bags of potato chips are randomly selected, what is the probability that their mean weight is between 5.5 oz to 6.5 oz?
d. If 40 bags of potato chips are randomly selected, what is the probability that their mean weight is less than 7.5 oz?