A machine that packages 500-gram boxes of sugar-coated wheat cereal is being studied. The weights for a random sample of 100 boxes of cereal packaged by this machine are given in the attached file.

The quality control analyst wants to estimate the actual amount of sugar-coated wheat cereal contained in 500-gram boxes produced. It is known from the manufacturing specifications that the standard deviation of the amount of wheat cereal is equal to 9.4 grams. 

1. Set up a 99% confidence interval estimate of the population mean wheat cereal weight.

2. On the basis of your results, do you think that the quality control analyst has a right to complain to the production manager? Why?

3. Does the population amount of sugar-coated wheat cereal per box have to be normally distributed here? Explain.

4. Explain why an observed value of 509.4grams for an individual box is not unusual, even though it is outside the confidence interval you calculated.

5. Suppose that you used a 95% confidence interval estimate. What would be your answers to 1.1 and 1.2?