Answer:
![L = 3.975](https://tex.z-dn.net/?f=L%20%3D%203.975)
Step-by-step explanation:
Given
See comment for data
Required
The lower limit 94% confidence interval
First, calculate the mean
![\bar x =\frac{\sum x}{n}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%5Cfrac%7B%5Csum%20x%7D%7Bn%7D)
![\bar x =\frac{0.9+10+0.9+8.7+4.8+2.6+1+13.3+9.5+8.9+8.9+4.6}{12}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%5Cfrac%7B0.9%2B10%2B0.9%2B8.7%2B4.8%2B2.6%2B1%2B13.3%2B9.5%2B8.9%2B8.9%2B4.6%7D%7B12%7D)
![\bar x =\frac{74.1}{12}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%5Cfrac%7B74.1%7D%7B12%7D)
![\bar x =6.175](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D6.175)
Next, calculate the standard deviation using:
![\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%28x%20-%20%5Cbar%20x%29%5E2%7D%7Bn%7D%7D)
So, we have:
![\sigma = \sqrt{\frac{(0.9 - 6.175)^2 +(10- 6.175)^2 +.................+(8.9- 6.175)^2 +(4.6- 6.175)^2}{12}}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cfrac%7B%280.9%20-%206.175%29%5E2%20%2B%2810-%206.175%29%5E2%20%2B.................%2B%288.9-%206.175%29%5E2%20%2B%284.6-%206.175%29%5E2%7D%7B12%7D%7D)
![\sigma = \sqrt{\frac{197.2625}{12}}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cfrac%7B197.2625%7D%7B12%7D%7D)
![\sigma = \sqrt{16.4385416667}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B16.4385416667%7D)
![\sigma = 4.054](https://tex.z-dn.net/?f=%5Csigma%20%3D%204.054)
For 94% interval, the z score is
![z = 1.88](https://tex.z-dn.net/?f=z%20%3D%201.88)
So, the margin of error (E) is:
![E = z * \frac{\sigma}{\sqrt n}](https://tex.z-dn.net/?f=E%20%3D%20z%20%2A%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%20n%7D)
![E = 1.88 * \frac{4.054}{\sqrt {12}}](https://tex.z-dn.net/?f=E%20%3D%201.88%20%2A%20%5Cfrac%7B4.054%7D%7B%5Csqrt%20%7B12%7D%7D)
![E = 1.88 * \frac{4.054}{3.464}](https://tex.z-dn.net/?f=E%20%3D%201.88%20%2A%20%5Cfrac%7B4.054%7D%7B3.464%7D)
![E = 2.200](https://tex.z-dn.net/?f=E%20%3D%202.200)
The confidence interval of the true mean is:
![CI = (\bar x \± E)](https://tex.z-dn.net/?f=CI%20%3D%20%28%5Cbar%20x%20%5C%C2%B1%20E%29)
The lower limit (L) is:
![L = \bar x -E](https://tex.z-dn.net/?f=L%20%3D%20%5Cbar%20x%20-E)
![L = 6.175 -2.200](https://tex.z-dn.net/?f=L%20%3D%206.175%20-2.200)
![L = 3.975](https://tex.z-dn.net/?f=L%20%3D%203.975)
and the upper limit (U) is
![U = \bar x + E](https://tex.z-dn.net/?f=U%20%3D%20%5Cbar%20x%20%2B%20E)
![U = 6.175 + 2.200](https://tex.z-dn.net/?f=U%20%3D%206.175%20%2B%202.200)
![U = 8.375](https://tex.z-dn.net/?f=U%20%3D%208.375)
-3,-4 is the answer “convert the rectangular coordinates (3,4) into polar coordinates
Use these conversions:
1 foot = 12 in
1 mile = 5280 feet
67000 in * [1 ft /12 in] * [1 mile/5280 ft]
Then the answer is the option c.
4/8-3/8=1/8more
Therefore Keith at 1/8 more of the sandwich than Henry.