Question: The fuel consumption of a certain type of vehicle is approximately normal, with standard deviation 3 miles per gallon. If a sample of 64 vehicles has an average fuel consumption of 16 miles per gallon:
(a) Determine a 95% confidence interval for the mean fuel consumption of all vehicles of this type.
(b) With 95% confidence, what is the possible error if the mean fuel consumption is taken to be 16 miles per gallon?
(c) How large a sample is needed if we wish to be 95% confident that the mean will be within 0.5 miles per gallon of the true mean?