Before 1900, the Chicago River's two branches, namely North Branch and South Branch, converged in downtown Chicago and flowed into Control Lake Michigan. An ambitious civil engineering project was undertaken Structure to reverse the flow to connect the Great Lakes to the Mississippi River A + B Basin, which led to better security of the city's water supply. In order to reverse the flow, a control structure was placed downstream of the confluence of the two branches. Proper design of the control structure required a complete understanding of the flow sources. Define the following random variables: A: North Branch flow speed has uniform distribution from 0.1 m/s to 2.5 m/s. XA: sample mean flow speed for 32 random measurements of the North Branch. . . B: South Branch flow speed is normally distributed with mean MB = 1.7 m/'s and standard deviation OB = 0.5 m/s. XB: sample mean flow speed for 17 random measurements of the South Branch. S: sample variance for the 17 random measurements of the South Branch. a. Compute the population mean flow speed for the North Branch, HA. b. Compute the population variance for the North Branch, of. c. Calculate the probability that the sample mean flow speed for the North Branch is greater than the sample mean flow speed for the South Branch, i.e. P(XA - XB > 0). d. Briefly describe the validity of applying the Central Limit Theorem for part (c). . Assume the two samples are collected, resulting with the North Branch sample mean greater than the South Branch sample mean. Based on these sample statistics and your answer to part (c), is this evidence to reject the form of the probability distributions and/or population parameters? Briefly justify your answer. f. Calculate the probability that the sample variance for the South Branch is greater than 0.5, i.e. P(S, > 0.5)