Answer: ![(2.8,\ 3.6)](https://tex.z-dn.net/?f=%282.8%2C%5C%203.6%29)
Step-by-step explanation:
The confidence interval for population mean is given by :-
![\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
Given : Sample size : n= 51 ( >30 , that means its a large sample)
Sample mean : ![\overlien{x}=3.2\text{ grams}](https://tex.z-dn.net/?f=%5Coverlien%7Bx%7D%3D3.2%5Ctext%7B%20grams%7D)
Standard deviation : ![\sigma=1.1\text{ grams}](https://tex.z-dn.net/?f=%5Csigma%3D1.1%5Ctext%7B%20grams%7D)
Significance level : ![1-0.99=0.01](https://tex.z-dn.net/?f=1-0.99%3D0.01)
Critical value : ![z_{\alpha/2}=\pm2.576](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D%5Cpm2.576)
Now, the 99% confidence interval for the mean grams of sugar will be :-
![=3.2\pm(2.576)\times\dfrac{1.1}{\sqrt{51}}\\\\\approx3.2\pm0.40\\\\=(2.8,\ 3.6)](https://tex.z-dn.net/?f=%3D3.2%5Cpm%282.576%29%5Ctimes%5Cdfrac%7B1.1%7D%7B%5Csqrt%7B51%7D%7D%5C%5C%5C%5C%5Capprox3.2%5Cpm0.40%5C%5C%5C%5C%3D%282.8%2C%5C%203.6%29)
Hence, the 99% confidence interval for the mean grams of sugar
= ![(2.8,\ 3.6)](https://tex.z-dn.net/?f=%282.8%2C%5C%203.6%29)
Option: step 2.
Because the student divided only the right side by 2. If you divide one side by a number you have to do the same with the other side to maintain the equality.
Multiply out : take the first number in the first box (6x) in (6x+4) and multiply it by both numbers in the second box
![36x^2-24x](https://tex.z-dn.net/?f=36x%5E2-24x)
then do the same with the second number in the first box
24x-16
then add those two together
Answer:
1 166/264
Step-by-step explanation: