Employees at a factory were divided into two groups. All employees had similar work experience on the assembly line. One group, Group T was given a new tool to use on the assembly line. People in this group would be expected to be able to complete an assembly slightly faster. The rest of the employees, Group P, did not have the tool and typically took more time to complete the task. Each of the histograms below show the distribution of completion times, in minutes, for one of the two groups. Histogram I Histogram II Frequency 14 12 2086 420 Frequency 14 12- 10- 8- 20 35 45 55 65 75 85 95 105115 Completion Time 35 45 55 65 75 85 95 105115 Completion Time (a) Of the two histograms shown, I and II, which is more likely to be the distribution of completion times for the students in Group P? Justify your answer. (b) Describe the shape of a histogram created from the data of the two groups of students combined. (c) Consider the population of all employees on the assembly line who are given the task of assembling one item. The distribution of the completion times has a shape similar to the combined histogram of students at the high school, with mean 70 minutes and standard deviation 26.5 minutes. For random samples of 50 students taken from the population, describe the sampling distribution of the sample mean completion time. (d) Consider the population T. Let xT be the mean of the 40 employees sampled, which is 48 minutes and let sigT be the standard deviation of those employees in population T, which is 12 minutes. Consider population P. Let xP be the mean assembly time of 50 employees sampled, which is 100 minutes, and let sigP be standard deviation of those employees in population P, which is 15 minutes. Find the mean and standard deviation of the sampling distribution for xT-xP.