A specialty company is in the business of preparing raw gemstones for use in jewelry. Processing gemstones involves first cutting, then polishing the stone (in that order). The amount of time it takes to complete each task is normally distributed with mean and standard deviation given in the table below.

Task Mean (minutes) Standard Deviation (minutes)

Cutting 13 6

Polishing 6 2

What is the probability that cutting the stone takes less than 10 minutes? b. What is the probability that polishing the stone takes less than 5 minutes? c. What is the probability that the entire process takes less than 15 minutes, assuming that there is no time between tasks? Hint: the process requires both cutting and polishing, one after the other, in that sequence. d. A quality control analyst measures the time it takes to cut and polish a random sample of 13 gemstones (recall that there is no time between tasks). What is the probability that the entire process takes less than 15 minutes for most of the 13 stones in this sample? Hint: the entire process requires completion of each task one after the other in the sequence shown. e. For the same sample of 13 stones, what is the probability that the sample mean for the entire process is less than 15 minutes? Hint: the process requires both cutting and polishing, one after the other, in that sequence.