6.10 Exercises ( please solve the question using R code and please provide the code)

1. We assume that the probability distribution of blood pressure, X, is N (, 2) distribution. Suppose we know that = 6. To estimate , we randomly selected 9 people and measured their blood pressure. The sample mean is x = 110.

(a) Write down the sampling distribution of the sample mean X and find its standard deviation. (b) Find the 80% confidence interval estimation for .

2. For the above question, suppose that we did not know and estimated it using the sample standard deviation s = 6. (a) Find the standard error for the sample mean as the estimator of the population mean. (b) Find the 80% confidence interval estimation for based on this sample