The standard deviation for a population is σ=5.10. A random sample selected from this population gave a mean equal to 80.20. The population is known to be normally distributed. (a) Determine a 99% confidence interval for μ by assuming n=16. [4 marks] (b) Determine a 99% confidence interval for μ by assuming n=25. [4 marks] (c) Does the width of the confidence intervals constructed in parts (a) and (b) decrease as the sample size increases? Explain.