For each of the following situations, calculate a \(95 \%\) confidence interval for the mean ( \(\sigma\) known), beginning with the step, "Identify the critical value of \(z\). ."

a. \(\bar{X}=7.00, \sigma_{\bar{X}}=1.00\)

b. \(\bar{X}=65.50, \sigma_{\bar{X}}=2.18\)

c. \(\bar{X}=26.40, \sigma_{\bar{X}}=1.05\)

d. \(\bar{X}=112.00, \sigma_{\bar{X}}=10.13\)