3. A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with σ2 = 1000 (psi)2 . A random sample of 12 specimens has a mean compressive strength of 3250 psi. (a) Construct a 95% two-sided confidence interval on the mean compressive strength. (b) Suppose it is desired to estimate the mean compressive strength with an error that is less than 15 psi at 99% confidence. What is the sample size required?