Question: the posted speed limit on a particular segment of an...

The posted speed limit on a particular segment of an interstate highway is 65 mph. From past experience, the standard deviation of vehicle speed is 10 mph. To estimate the average speed of vehicles, the speeds of 50 vehicles are recorded and the average speed is estimated to be 67 mph. (1) Determine the 95% confidence interval for the mean vehicle speed; 2) The confidence level of the confidence interval estimated in (1) needs to be increased from 95% to 99%. How many additional measurements are required? (Hint: the confidence intervals are the same for the two cases)