36. Traffic speed, part 2. The speed-measuring machines must measure accurately to maximize effectiveness in slowing traffic. The accuracy of the machines will be tested before placement on city streets. To ensure that error rates are estimated accurately, the researchers want to take a large enough sample to ensure usable and accurate interval estimates of how much the machines may be off in measuring actual speeds. Specially, the researchers want the margin of error for a single speed measurement to be no more than mph.

a) Discuss how the researchers may obtain a reasonable estimate of the standard deviation of error in the measured speeds.

b) Suppose the standard deviation for the error in the measured speeds equals 4 mph. At 95% confidence, what sample size should be taken to ensure that the margin of error is no larger than mph?