The diameters of Red Delicious apples in a certain orchard are normally distributed with a mean of 2.63 inches and a standard deviation of 0.25 inches.
a. What percentage of the apples in the orchard have diameters less than 1.95 inches?
b. What percentage of the apples in the orchard have diameters larger than 2.90 inches?
c. If a crate of 200 apples is selected from the orchard, approximately how many apples would you expect to have diameters greater than 2.90 inches?
d. What is the probability that a randomly selected apple in this orchard will have a diameter larger than 2.54 inches?
e. What is the probability that a randomly selected apple in this orchard will have a diameter between 1.95 inches and 2.9 inches? Interpret the meaning of this answer.