A regional chain of fast-food restaurants would like to estimate the mean time required to serve its drive-thru customers.

a.	If the population standard deviation of service times is known to be 20 seconds, how large a sample must be used to estimate the mean service time for drive-thru customers if a margin of error of no more than 14 seconds of the true mean with a 95% level of confidence is required?
b.	Suppose the manager believes that a margin of error of 14 seconds is too high and has decided it should be cut inhalf to a margin of error of 7 seconds. The manager believes that by cutting the margin of error inhalf, the required sample size will double. Is the manager correct?