A point Q on a segment with endpoints A(2, −1) and C(4, 2) partitions the segment in a 3:1 ratio. Find Q. You must show all work to receive credit. (WORTH 100 POINTS)

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.