A company fills bags with fertilizer for retail sale. The weights of the bags of fertilizer have a normal distribution with a mean weight of 15 lbs and a standard deviation of 1.70 lbs.
a. What is the probability that a randomly selected bag of fertilizer will weigh between 14 and 16 pounds? (Use z for normal distribution.)
b. If 35 bags of fertilizer are randomly selected, find the probability that the average weight of the 35 bags will be between 14 and 16 lbs.