Question: 5. Let (X1, X2, . .., Xn) be a random sample from a Poisson()) distribution where A is an unknown parameter. (a) Suppose that the

5. Let (X1, X2, . .., Xn) be a random sample from a Poisson()) distribution where A is an unknown parameter. (a) Suppose that the sample size n is large. Find a pivotal variable in terms of the sample mean X and the parameter / using normal approximation based on the Central Limit Theorem. (b) Derive an approximate (1-a) x 100% confidence interval for A using the pivotal variable found in part (a). You may further approximate the unknown parameter in the variance term by its estimator. (c) Construct a 95% confidence interval for A if X = 1.5 from a random sample of size n = 36. 6. The manufacturer of a sports car wants to estimate p, the proportion of people in a given income bracket who will be interested in a particular new model, by constructing a confidence interval. (a With the same confidence level, which confidence interval do you prefer, a wider one or a narrower one? Why? (b) Suppose the company wants to obtain a narrow interval with 99% confidence level. What is the minimum required sample size which will assure the width of the confidence interval to be smaller than 0.1

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