Consider a population having a standard deviation equal to 10.07. We wish to estimate the mean of this population. [a] How large a random sample is needed to construct a 95 percent condence interval for the mean of this population with a margin of error equal to 1? [Round your answer to the next whole number.} The random sample is - units. lb} Suppose that we now take a random sample of the size we have determined in part a. If we obtain a sample mean equal to 277, calculate the 95 percent confidence interval for the population mean. What is the interval's margin of error? {Round your answers to the nearest 'whole number.) The 95 percent condence interval is [ ]. Margin of error