Question 1039097
Given information
x = 456 (number of successes)
n = 800 (sample size)
Confidence Level = 95%

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What we want to find: 

We want to find the lower (L) and upper (U) boundaries of the confidence interval

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The critical value of the 95% confidence interval is z = 1.96 (approximately). You can determine this by using a table like <a href="http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">this one</a>. Look at the confidence level 95% (bottom of page) then look directly above it to find the value of 1.960 which is the same as 1.96



Sample proportion 
p = x/n = 456/800 = 0.57



Standard Error (SE)
{{{SE = sqrt((p*(1-p))/n)}}}
{{{SE = sqrt((0.57*(1-0.57))/800)}}}
{{{SE = sqrt((0.57*(0.43))/800)}}}
{{{SE = sqrt(0.2451/800)}}}
{{{SE = sqrt(0.000306375)}}}
{{{SE = 0.01750357106421}}} 



Margin of Error (ME)
{{{ME = z*SE}}}
{{{ME = 1.96*0.01750357106421}}}
{{{ME = 0.03430699928586}}}



The lower boundary of the confidence interval is 
{{{L = p - ME}}}
{{{L = 0.57 - 0.03430699928586}}}
{{{L = 0.53569300071414}}}
That turns into 53.569300071414% which rounds to 53.57%


So L = 53.57% approximately 



The upper boundary of the confidence interval is 
{{{U = p + ME}}}
{{{U = 0.57 + 0.03430699928586}}}
{{{U = 0.60430699928587}}}
That turns into 60.430699928587% which rounds to 60.43%


So U = 60.43% approximately



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To recap, the lower and upper bound (L and U respectively) of the confidence interval is


L = 53.57%
U = 60.43% 


where the boundaries are in percentage form


Final Answer:
<font color=black><u>&nbsp;&nbsp;&nbsp;<font color=red>53.57</font>&nbsp;&nbsp;&nbsp;</u></font> to <font color=black><u>&nbsp;&nbsp;&nbsp;<font color=red>60.43</font>&nbsp;&nbsp;&nbsp;</u></font>%