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Question 1160843: Assume a normal distribution with known population variance. Calculate the lower
confidence limit (LCL) and upper confidence limit (UCL) for each of the following.
a. 𝑥̅ = 50; n = 64; 𝜎 = 40; α = 0.05
b. 𝑥̅ = 85; n = 225; 𝜎2 = 400; α = 0.01
c. 𝑥̅ = 510; n = 485; 𝜎 = 50; α = 0.10
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! half-interval is z*sigma/sqrt(n), and this is added and subtracted to and from the mean to get the interval limits.
half-interval for a is z(0.975)*40/sqrt(64)=9.8
(40.2, 59.8)
half-interval for b is z(0.995)*20/sqrt (225). Variance is sigma^2 so have to take the square root of 400 for sigma.
=2.576*20/15=3.43
(81.57, 88.43)
half-interval for c is z(0.95)*50/sqrt(485)
=1.645*50/sqrt (485)=3.73
(506.27, 513.73)
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