3. Let X1, ..., Xn follow a Poisson distribution with rate parameter A. It is known that the sample mean is a consistent estimator for A. Using the central limit theorem or otherwise, show that an approximate 95% confidence interval for A can be calculated using the sample mean statistic, x, as follows: 5 - 1.96 - a + 1.96 n n Give a reason why this is an approximate confidence interval rather than an exact interval