A local grocery chain reports that the annual consumption of fresh fruit per person is normally distributed with a mean of 46.25kg and a standard deviation of 3.5kg while the annual consumption of fresh vegetable per person is normally distributed with a mean of 47.50kg and a standard deviation of 4.5kg.

a) Suppose a researcher took a random sample of 49 people and had them keep a record of the fresh fruit they ate for one year. What is the probability that the mean annual consumption would be less than 45.25kg?

b) What is the probability that the average annual consumption of fresh fruit of 81 randomly selected people is higher than the average annual consumption of fresh vegetable of 64 randomly selected people?

c) A local grocery chain declares that 35% of the people consume fresh fruit. What is the probability that in a random sample of 60 people, less than 20% will consume fresh fruit?

d) Solve this part independently. The coordinator at the Frost library Glendon campus has asked her student assistant for an interval estimate of the mean number of books checked out each day. The assistant took a sample and found the mean to be 550 books. She provides the coordinator with an interval estimate of between 450 and 670 books checked out per day. An efficient, unbiased point estimate of the number of books checked out each day at the Frost library Glendon campus is?