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.​ Specifically, the researchers want the margin of error for a single speed measurement to be no more than mph. Complete parts a and b below. ​a) Discuss how the researchers may obtain a reasonable estimate of the standard deviation of error in the measured speeds. Choose the correct answer below.
A.
The researchers could perform the study with the maximum sample size and then find the standard deviation of the data.
B.
The researchers could pick a random number and see how well that fits the data.
C.
The researchers could look at previous studies or take preliminary pilot studies.
D.
The researchers could use a standard deviation that fits a lot of different sets of data.
​b) Suppose the standard deviation for the error in the measured speeds equals mph. At​ 95% confidence, what sample size should be taken to ensure that the margin of error is no larger than + or - 1.5 ​mph?
The sample size should be

​(Round up to the nearest whole​ number.)