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A store owner is interested in opening a second shop. She wants to estimate the true average daily revenue of her current shop to decide whether expanding her business is a good idea. The store owner takes a random sample of 60 days over a six-month period and finds that the mean revenue of those days is 3,472.00 dollars with variance 315,900.20 square dollars. Calculate a 95% confidence interval to estimate the true average daily revenue.

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Every confidence interval has associated z value. As confidence interval increases so do the z value associated with it. 
The confidence interval can be calculated using following formula:
[tex]\overline{x} \pm \frac{zs}{\sqrt n}[/tex]
Where [tex] \overline{x} [/tex] is the mean value, z is the associated z value, s is the standard deviation and n is the number of samples.
We know that standard deviation is simply a square root of variance:
[tex]s=\sqrt{315900.20}=\$562.05[/tex]
The confidence interval of 95% has associated z value of 1.960.
Now we can calculate the confidence interval for our income:
[tex]3472.00\pm \frac{1.960\cdot 562.05}{\sqrt{60}}\\ \$3472.00\pm142.22[/tex]


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