Answer to Question #147842 in Statistics and Probability for Shusmita shrestha

Question

A machine that fills cereal boxes is supposed to put 500 grams of cereal in each box. A simple random sample of 9 boxes is found to contain a sample mean of 490 grams of cereal. It is known from past experience that the fill weights are normally distributed with a standard deviation of 5 grams.
Construct a 90% confidence interval for the mean fill weight.

Answer 1

Population standard deviation is known, thus, Z is used.

$CI=\bar X \pm Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt{n}}$

$$Z_{0.05}=1.645$$

$CI=490 \pm 1.645\frac{5}{\sqrt{9}}$

$=490\pm 2.742$

={487.258,492.742}