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:
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:
Now we can calculate the lower and upper bound of the confidence interval as:
The 99.7% confidence interval for the mean price of all new mobile homes is ($60,672, $65,622).
