1. A company is designing its operations around their workers. We are told that the time taken by each group is normal. They have workers who have experience in similar positions and are older. This group is called Group I. The supervisor finds that the workers from Group 1 take, on average, 40 minutes with a standard deviation of 6 minutes. They have hired another group of workers who are younger and more energetic, but also more erratic. This is Group II. This second group gets intensive training before they are released on the production floor. The average for Group II is 38 minutes with a standard deviation of 10. a) (4) What is the probability that the sample mean of 9 workers from Group II would be between 30 and 48 minutes? b) (6) They set up two different shifts, with 25 workers in each. Shift I is made up of Group I workers. Shift II is made up of Group II workers. The groups are statistically independent. What is the probability that both shifts will take, on average, more than 42 minutes to complete the job