From what I understand with the problem, you are only asked to find the value of x which is the number of months. So, you don't really need a graph to answer this question. Just solve this like any other problem in algebra.
100 + 36x = C, where the maximum value of C is $352
100 + 36x = 352
36x = 352 - 100
36x = 252
x = 7 months
Therefore, x should be at most 7 months.
Answer:
The sample size required is 225.
Step-by-step explanation:
The confidence interval for population mean (<em>μ</em>) is:
![\bar x\pm z_{\alpha /2}\times \frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%20x%5Cpm%20z_%7B%5Calpha%20%2F2%7D%5Ctimes%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
The margin of error is:
![MOE= z_{\alpha /2}\times \frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=MOE%3D%20z_%7B%5Calpha%20%2F2%7D%5Ctimes%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
Given:
![\bar x=2.2\\\sigma=0.3](https://tex.z-dn.net/?f=%5Cbar%20x%3D2.2%5C%5C%5Csigma%3D0.3)
The margin of error is, <em>MOE</em> = 0.04
The confidence level is 95.44%.
The critical value of <em>z</em> for 95.44% confidence interval is:
![P(-2\leq Z\leq 2)=0.9544](https://tex.z-dn.net/?f=P%28-2%5Cleq%20Z%5Cleq%202%29%3D0.9544)
So,
.
Determine the sample size as follows:
![MOE= z_{\alpha /2}\times \frac{\sigma}{\sqrt{n}}\\0.04=2\times\frac{0.30}{\sqrt{n}}\\ n=(15)^{2}\\=225](https://tex.z-dn.net/?f=MOE%3D%20z_%7B%5Calpha%20%2F2%7D%5Ctimes%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C0.04%3D2%5Ctimes%5Cfrac%7B0.30%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C%20n%3D%2815%29%5E%7B2%7D%5C%5C%3D225)
Thus, the sample size required is 225.