The diameters of oranges in a certain orchard are normally distributed with a mean of 7.3 inches and a standard deviation of 0.80 inches. Describe all work.
A) What percentage of oranges in this orchard have diameters less than 6.7 inches?
B) What percentage of oranges in this orchard are larger than 7.20 inches?
C) A random sample of 100 oranges is collected and the mean diameter obtained was 7.20. If another sample of 100 is taken, determine the probability that its sample mean will be greater than 7.10 inches?
D) Why is the z-score employed in answering (A), (B), and (C)?
E) Why is the formula for z employed in (C) different from that employed in (A) and (B)?