Answer: The required confidence interval is (56.1,66.9).
Step-by-step explanation:
Since we have given that
53.1, 60.2, 60.6, 62.1, 64.4, 68.6
![\bar{x}=\dfrac{53.1+60.2+60.6+62.1+64.4+68.6}{6}=\dfrac{369}{6}=61.5](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%3D%5Cdfrac%7B53.1%2B60.2%2B60.6%2B62.1%2B64.4%2B68.6%7D%7B6%7D%3D%5Cdfrac%7B369%7D%7B6%7D%3D61.5)
n = 6
Margin of error = 5.4
At 95% level of confidence, z = 1.96
So, the confidence interval would be
![\bar{x}\pm \text{Margin of error}\\\\=61.5\pm 5.4\\\\=(61.5-5.4,61.5+5.4)\\\\=(56.1,66.9)](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%5Cpm%20%5Ctext%7BMargin%20of%20error%7D%5C%5C%5C%5C%3D61.5%5Cpm%205.4%5C%5C%5C%5C%3D%2861.5-5.4%2C61.5%2B5.4%29%5C%5C%5C%5C%3D%2856.1%2C66.9%29)
Hence, the required confidence interval is (56.1,66.9).