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.
A) [1.20, 1.24]
B) [1.18, 1.26]
C) [1.16, 1.28]
D) [1.14, 1.30]

Question

Quizplus · Accepted Answer

The 95% confidence interval for the mean can be calculated using the formula: $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $Z$ is the Z-score corresponding to the confidence level (for 95%, $Z = 1.96$), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $1.22 \pm 1.96 \frac{0.06}{\sqrt{36}} = 1.22 \pm 0.02$, which gives the interval [1.20, 1.24].

A Machine That Is Programmed to Package 1