A random sample of n measurements was selected from a population with unknown mean and standard deviation = 20. Calculate a 95% confidence

A random sample of n measurements was selected from a population with unknown mean µ and standard deviation σ = 20. Calculate a 95% confidence interval for µ for each of the following situations:
a. n = 75, x̅ = 28
b. n = 200, x̅ = 102
c. n = 100, x̅ = 15
d. n = 100, x̅ = 4.05
e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a-d? Explain.