Problem 2 (6 points) A random sample of 120 healthy pine tree heights yielded a sample average of 185 feet with a sample standard deviation of 5 feet. (a) (2 points) Derive the formula for a 100(1 -o)% confidence interval for the population average. (b) (1 point) Give a 95% confidence interval for the average height of healthy pine trees. (c) (1 point) Give a 99% confidence interval for the average height of healthy pine trees. (d) (1 points) Based on your answers to (b) and (c) what is the relationship between confidence level and interval width? Will this always be the case? (e) (1 points) Do either of the confidence intervals computed contain the average height of healthy pine trees, 180 feet? What conclusions could we draw from this observation