The average speed of vehicles on a freeway is being studied. Assume that the standard deviation of vehicle speed is known to be 8 km/h.

(a) Suppose observations on 120 vehicles yielded a sample mean of 105 km/h. determine two-sided 99.5% confidence intervals of the mean speed. (Assume a normal distribution).

(b) In part (a), how many additional vehicles' speed should be observed such that the mean speed can be estimated to within ±1 km/h with 99.5% confidence?

(c) Suppose Jason and Britney are assigned to collect data on the speed of vehicles on this highway. After each person has separately observed 60 vehicles, what is the probability that Jason's sample mean will be equal to Britney's sample mean ±0.5 km/h?

(d) Repeat part (c) if each person has separately observed 120 vehicles instead.