The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.82 inches and a standard deviation of 0.61 inches. Show all work.
(A) What percentage of the grapefruits in this orchard is larger than 5.78 inches?
(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample is greater than 5.78 inches?