Answer to Question #268072 in Statistics and Probability for EMB

Question

A paint manufacturer uses a machine to fill gallon cans with paint. The manufacturer wants to estimate the mean volume of paint of the machine is putting in the cans within 0.06 ounce. Determine the minimum sample size required to construct a 85% confidence interval for the population mean. Assume the population standard deviation is 0.82 ounce.

Answer 1

If $\bar{x}$ is used as an estimate of $\mu,$ we can be $100(1-\alpha)$% confident that the error $|\bar{x}-\mu|$

will not exceed a specified amount $E$ when the sample size is

$$n\geq(\dfrac{z_{\alpha/2}\sigma}{E})^2$$

Given 85% confidence interval, $z_{\alpha/2}=1.4395$

$E=0.06, \sigma=0.82$

$$n\geq(\dfrac{1.4395(0.82)}{0.06})^2$$

$$n\geq387.0335$$

$n=388$