Question

A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Find the 95% confidence interval for the mean.

Answer 1

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

$\bar{X}=1.22\ pounds$

$\sigma=0.06\ pounds$

n= 36

We need to find the 95% confidence interval for the mean.

So, z = 1.96

So, confidence interval would be

$\bar{x}\pm z\dfrac{\sigma}{\sqrt{n}}\\\\=1.22\pm 1.96\times \dfrac{0.06}{\sqrt{36}}\\\\=1.22\pm 1.96\times \dfrac{0.06}{6}\\\\=1.22\pm 1.96\times 0.01\\\\=1.22\pm 0.0196\\\\=(1.22-0.0196,1.22+0.0196)\\\\=(1.2004,1.2396)$

Hence, the 95% confidence interval for the mean is (1.2004, 1.2396).