Answer: Hence, the 95% confidence interval for the mean is (1.2004, 1.2396).
Step-by-step explanation:
Since we have given that
Mean = μ = 1.20 pounds
[tex]\bar{X}=1.22\ pounds[/tex]
[tex]\sigma=0.06\ pounds[/tex]
n= 36
We need to find the 95% confidence interval for the mean.
So, z = 1.96
So, confidence interval would be
[tex]\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=1.22\pm 1.96\times \dfrac{0.06}{\sqrt{36}}\\\\=1.22\pm 1.96\times \dfrac{0.06}{6}\\\\=1.22\pm 1.96\times 0.01\\\\=1.22\pm 0.0196\\\\=(1.22-0.0196,1.22+0.0196)\\\\=(1.2004,1.2396)[/tex]
Hence, the 95% confidence interval for the mean is (1.2004, 1.2396).
