Question 865293
Use <a href="http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg">this table</a> to get the critical value of {{{z = 1.960}}} (look in the row that starts with {{{infinity}}}. In this row, you'll find a value that's above the 95% confidence level, which is 1.960)



The sample mean is xbar = 25577 (given)
The population standard deviation is sigma = 2566 (given)
The sample size is n = 400 (given)
From above, the critical value for a 95% confidence interval is z = 1.960 (this is approximate)



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We will use these values to plug them into the lower bound L and upper bound U formulas below



L = xbar - z*sigma/sqrt(n)
U = xbar + z*sigma/sqrt(n)



where the confidence interval is [L, U]



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Now let's find the lower bound L of the confidence interval



L = xbar - z*sigma/sqrt(n)



L = 25577 - 1.960*2566/sqrt(400)



L = 25577 - 251.468



L = 25325.532



L = 25326



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Now let's find the upper bound U of the confidence interval



U = xbar + z*sigma/sqrt(n)



U = 25577 + 1.960*2566/sqrt(400)



U = 25577 + 251.468



U = 25828.468



U = 25828



So the confidence interval [L,U] is [25326, 25828]



This is <font color="red">choice A)  [$25,326, $25,828]</font>