Question 1179095
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Hi
x̄ - ME < {{{mu}}} < x̄ + ME
A 99% confidence interval...
65.7 < μ < 67.3   | ME = (67.3-65.7)/2 = 1.6/2 = .8
x̄ = 66.5
ME ={{{ z*sigma/sqrt(n)}}}
 .8 = {{{ 2.576*sigma/12}}}
 (.8)(12) /2.576 = σ = 3.727

Construct the 95% confidence interval. 
ME ={{{ z*sigma/sqrt(n)}}} = 1.96*(3.727)/12 = .6 (rounded to nearest tenth)
x̄ - ME < {{{mu}}} < x̄ + ME
66.5 - .6 < {{{mu}}} < 66.5 +.6
  65.9  < {{{mu}}} < 67.1
Wish You the Best in your Studies.
 = CI	z = value
90%	z =1.645
92%	z = 1.751
95%	z = 1.96
98%	z = 2.326
99%	z = 2.576

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