Consider a population having a standard deviation equal to 9.76. 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.)

(b)Suppose that we now take a random sample of the size we have determined in parta. If we obtain a sample mean equal to 331, 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.)