6.2 (modified) The average speed of vehicles on a highway is being studied. Suppose observations on 50 vehicles yielded a sample mean of 105 km/h. Assume that the standard deviation of vehicle speed is known to be 9.7 km/h. (a) Determine the two-sided 99% confidence interval of the mean speed. (b) How many additional vehicles' speed should be observed such that the mean speed can be estimated to within +1.6 km/h with 99% confidence? (c) Suppose John and Mary are assigned to collect data on the speed of vehicles on this highway. After each person has separately observed 10 vehicles, what is the probability that John's sample mean will exceed Mary's sample mean by 3 km/h? (d) The mayor claim that the speed of vehicles on the highway does not exceed 110 km/h. Can his claim be supported at the 5% significance level