Confidence Intervals Questions and Answers

According to the Central Limit Theorem, for a sufficiently large sample size $n$ drawn from any population with mean $\mu$ and variance $\sigma^2$, the distribution of the sample mean $\bar{X}$ is approximately

120 bags of mealie-meal have mean mass 750g and standard deviation 3.9g. What is the standard error of the mean, correct to 3 decimal places?

120 bags of mealie-meal have mean mass 750g and standard deviation 3.9g. Using a 95% confidence interval with $z = 1.96$, what is the upper bound of the confidence interval for the mean mass, in grams, correct to 2 decimal places?

The diameters of 25 steel rods have a sample mean of 0.980 cm and a standard deviation of 0.015 cm. Assuming the diameters are normally distributed with this standard deviation, find the 99% confidence interval for the population mean diameter.