Answer:
The sample size must be approximately 1304.
Step-by-step explanation:
We are given the following in the question:
Population standard deviation = 15,500 miles
We have to construct a 92% confidence interval with margin of error of 1000 miles.
Margin of error =
[tex]z_{critical}\times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.02} = \pm 2.33[/tex]
Putting values, we get,
[tex]2.33\times \dfrac{15500}{\sqrt{n}} = 1000\\\\\sqrt{n} = 2.33\times \dfrac{15500}{1000} \\\sqrt{n} = 36.115\\n = 1304.29\\n\approx 1304[/tex]
The sample size must be approximately 1304.
