1. Consider a continuous random variable X with Var(X) = 4. A sample of 50 measurements of X is taken and Xbar = 68
a. Which distribution is followed by X ? What are its parameters? (if you cannot give the parameter(s), then give point(s) estimate using the appropriate notation)
b. Which distribution is followed by Xbar? What are its parameters? (if you cannot give the parameter(s), then give point(s) estimate using the appropriate notation)
c. Calculate the interval for 95% confidence on the mean of X? What is the interpretation of this interval?
d. Calculate the interval for 89% confidence on the mean of X? What is the interpretation of this interval?
e. How confident are you that the mean of X is between 67.706 and 68.293