The standard deviation for a population is = 7.14. A random sample selected from this population

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