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 :t: 10 seconds of the true mean with a 90% level of condence is required? b. Suppose the manager believes that a margin of error of :t 10 seconds is too high and has decided it should be cut by four fths to a margin of error of :t 2 seconds. The manager believes that by cutting the margin of error by four fths, the required sample size will quintuple. Is the manager correct? a. The sample size must be at least |:|. (Round up to the nearest whole number.) b. The manager V correct. The required sample size for the smaller margin of error is V times the sample size required for the larger margin of error