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. \(\bar{X}=50.00, \sigma_{\bar{X}}=3.00\)

b. \(\bar{X}=1.58, \sigma_{\bar{X}}=.12\)

c. \(\bar{X}=7.34, \sigma_{\bar{X}}=1.87\)

d. \(\bar{X}=32.56, \sigma_{\bar{X}}=3.70\)