Answer:
The 99.7% confidence interval for the mean price of all new mobile homes is ($60,672, $65,622).
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>The prices in thousands of dollar are:</em>
<em>66.6, 69.8, 58.4, 57.3, 63.1, 61.8, 56, 72.7, 61.8, </em>
<em>66.9, 72.6, 63.1, 58.7, 65.9, 61.1, 56.1, 49.9, 72.6, </em>
<em>49, 56.4, 72.6, 60.1, 65, 64.8, 56.5, 52, 53.2, </em>
<em>56.4, 75.4, 76.3, 60.5, 74.6, 57, 69.2, 62.7, 77.2.</em>
<em />
We have a sample of n=36 new mobile homes.
The mean of this sample is:
![M=(1/36)\sum_{i=1}^{36}x_i=\dfrac{2273.3}{36}=63.147](https://tex.z-dn.net/?f=M%3D%281%2F36%29%5Csum_%7Bi%3D1%7D%5E%7B36%7Dx_i%3D%5Cdfrac%7B2273.3%7D%7B36%7D%3D63.147)
The population standard deviation is σ=7.5 (in thousands of dollars).
The critical value of z for a 99.7% CI is z=2.97.
Then, we can calculate the margin of error as:
![E=z\cdot \sigma/\sqrt{n}=2.97*7.5/\sqrt{36}=22.275/9=2.475](https://tex.z-dn.net/?f=E%3Dz%5Ccdot%20%5Csigma%2F%5Csqrt%7Bn%7D%3D2.97%2A7.5%2F%5Csqrt%7B36%7D%3D22.275%2F9%3D2.475)
Now we can calculate the lower and upper bound of the confidence interval as:
![LL=\bar X-E=63.147-2.475=60.672\\\\UL=\bar X+E=63.147+2.475=65.622](https://tex.z-dn.net/?f=LL%3D%5Cbar%20X-E%3D63.147-2.475%3D60.672%5C%5C%5C%5CUL%3D%5Cbar%20X%2BE%3D63.147%2B2.475%3D65.622)
The 99.7% confidence interval for the mean price of all new mobile homes is ($60,672, $65,622).