Answers to three decimal places please.

The length of wire, X, needed to hang a 12-inch by 16-inch painting is normally distributed with unknown mean, u inches and known standard deviation o = 0.75 inches. We wish to create a confidence interval for u. We randomly select 13 such paintings and measure the amount of wire used in each. The sample gave a sample mean of x = 12.61 inches and a sample standard deviation s = 0.75 inches. a)What is the critical value for a 95.0% confidence interval for u? b) Create a 95.0% confidence interval for u c) How long (in inches) is the 95.0% confidence interval for M? d) How many observations would we need to guarantee that the 95.0% confidence interval has a length of 0.5 inches or less? e) Create a 95.0% prediction interval for a single future randomly chosen 12x16 inch painting. f) Assuming o is not known, create a 95.0% confidence interval for u using this data. g. What is the length (inches) of the confidence interval for part f