Calculate the lower confidence limit (lcl) and upper confidence limit (ucl) of the mean for each of the following. a. x =265, n=459, σ=50, and α=0.01b. x=180, n=308, σ2equals=100, and α=0.05lclequals=(round to two decimal places as needed.)uclequals=(round to two decimal places as needed.)b. lclequals=(round to two decimal places as needed.)uclequals=(round to two decimal places as needed.)

a: 258.09

b: 178.88

Step-by-step explanation:

For a:  Since n > 30, we use a z-value that corresponds to 0.01, or 99% confidence.  This z-value is: 2.575

We have:

x = 265, n = 459, σ = 50.  See the calculation for the error and the construction of the confidence interval on the first attached photo

For b:  Since n > 30, we use a z-value that corresponds to 0.05, or 95% confidence.  This z-value is: 1.96

x = 180, n = 308, σ = 10  (it gives σ² = 100. so σ = 10).  See the calculation for the error and the construction of the confidence interval on the second attached photo

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step-by-step explanation: