Consider a population having a standard deviation equal to 10.12. 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.)

n=394

(a) was solved. need help with (b)

(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 254, 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.)