2. The standard deviation for a population is 7.14. A random sample selected from this population gave a mean equal to 48.52. a. Make a 95% confidence interval for the population mean assuming a sample of size 196. b. Construct a 95% confidence interval for the population mean assuming a sample of size 100. c. Determine a 95% confidence interval for the population mean assuming a sample of size 49. d. Does the width of the confidence intervals constructed in parts a through c increase as the sample size decreases? Explain