Question

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.)

Answer 1

a: 258.09

b: 178.88

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