Answer :
Answer:
The sample size should be approximately 553 to have a margin of error of 0.5
Step-by-step explanation:
We are given the following in the question:
Population standard deviation = 6 gallons.
Margin of error = 0.5
95% confidence interval:
[tex]\mu \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]
Margin of error =
[tex]z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting the values, we get,
[tex]0.5 = 1.96\times \dfrac{6}{\sqrt{n}}\\\\\sqrt{n} = 1.96\times \dfrac{6}{0.5}\\\\n = (1.96)^2\times \dfrac{36}{0.25}\\\\n = 553.1904\\n \approx 553[/tex]
Thus, the sample size should be approximately 553 to have a margin of error of 0.5