Answer:
For a sample size of 10, the t-value is about 3.25 (from tables) at a 99% confidence interval.
Explanation:
When the standard deviation for the population is not known, the confidence interval estimate for the population mean is performed with the Student's t-distribution.
The confidence interval for the mean is calculated as
![(\Bar{x}- t\frac{s}{\sqrt{n}} , \, \Bar{x}+ t\frac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=%28%5CBar%7Bx%7D-%20t%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%20%2C%20%5C%2C%20%5CBar%7Bx%7D%2B%20t%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%20)
where
![\Bar{x}](https://tex.z-dn.net/?f=%5CBar%7Bx%7D)
= sample mean,
s = sample standard deviation,
t = t-value (provided in tables),
n = sample size.
When reading the t-value, (n-1) is called the df or degrees of freedom.
Given:
Radius of the cone = 3 inches
Height of the cone = 8 inches
To find:
The volume of the cone, in terms of π.
Solution:
We know that, the volume of a cone is:
![V=\dfrac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
Putting
, we get
![V=\dfrac{1}{3}\pi (3)^2(8)](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20%283%29%5E2%288%29)
![V=\dfrac{1}{3}\pi (9)(8)](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20%289%29%288%29)
![V=\dfrac{72}{3}\pi](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B72%7D%7B3%7D%5Cpi%20)
![V=24\pi](https://tex.z-dn.net/?f=V%3D24%5Cpi%20)
Therefore, the volume of the cone is
.
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150*5.5=825
If I'm right, the actual length of the border is 825 miles. Hope I helped!