Find the LCL and UCL for themean of each of the following when the draws are kno

Question

Find the LCL and UCL for themean of each of the following when the draws are known to befrom
a normal distribution with the specified variance.
(a) a = 0.05; n = 25; x = 500; s = 30
(b) a = 0.05; n = 50; x = 500; s = 30
(c) a = 0.10; n = 25; x = 500; s = 30

Explanation / Answer

(a) Given =0.05, |Z(0.025)|=1.96 (check normal table) The 95% CI is xbar ± Z*s/n --> 500 ± 1.96*30/sqrt(25) --> ( 488.24, 511.76) So LCL is 488.24 UCL is 511.76 ---------------------------------------------------------------------------------------------- (b)Given =0.05, |Z(0.025)|=1.96 (check normal table) The 95% CI is xbar ± Z*s/n --> 500 ± 1.96*30/sqrt(50) --> ( 491.6844, 508.3156) So LCL is 491.6844 UCL is 508.3156 ---------------------------------------------------------------------------------------------- (c) Given =0.1, |Z(0.05)|=1.645 (check normal table) The 95% CI is xbar ± Z*s/n --> 500 ± 1.645*30/sqrt(25) --> ( 490.13, 509.87) So LCL is 490.13 UCL is 509.87

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