A random sample of n measurements was selected from a population with unknown mean and known

A random sample of n measurements was selected from a population with unknown mean μ and known standard deviation σ. Calculate a 95% confidence interval for μ for each of the following situations:

a. n = 75, x̄ = 28, σ² = 12

b. n = 200, x̄ = 102, σ² = 22

c. n = 100, x̄ = 15, σ = .3

d. n = 100, x̄ = 4.05, σ = .83

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.