A store owner is interested in opening a second shop. She wants to estimate the true average daily revenue of her current shop t

Question

1 month ago

7

A store owner is interested in opening a second shop. She wants to estimate the true average daily revenue of her current shop t

o 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.

Mathematics

1 answer:

babunello [11.8K] · Answer 1 · 2026-02-21T17:40:50+03:00

Every confidence interval correlates with a specific z value. As the confidence interval expands, so does the corresponding z value.
You can compute the confidence interval using the formula:
$\overline{x} \pm \frac{zs}{\sqrt n}$
Here $\overline{x}$ represents the mean, z is the respective z value, s denotes the standard deviation, and n indicates the sample size.
Standard deviation is simply the square root of variance:
$s=\sqrt{315900.20}=\$562.05$
For a confidence interval of 95%, the z value is <span>1.960.
</span>Now, we can compute the confidence interval for our income:
$3472.00\pm \frac{1.960\cdot 562.05}{\sqrt{60}}\\ \$3472.00\pm142.22$