Consider a population having a standard deviation equal to 10.05. we wish to estimate the mean of this population. (a) how large a random sample is needed to construct a 95 percent confidence 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. (b) 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 252, calculate the 95 percent confidence interval for the population mean. what is the interval’s margin of error?