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Answer:
The 99% confidence interval for the average length of time all car owners plan to keep their cars is between 3.85 years and 10.55 years.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 7.2 - 3.35 = 3.85 years
The upper end of the interval is the sample mean added to M. So it is 7.2 + 3.35 = 10.55 years
The 99% confidence interval for the average length of time all car owners plan to keep their cars is between 3.85 years and 10.55 years.