Describe the Central Limit Theorem and state the condition usually required for its application.
A boutique apiary produces jars of organic honey. The mass of honey in a jar is a random variable with a known population standard deviation of 4.5 g. A trading standards officer selects a random sample of 81 jars and records the total mass of honey as ∑m=40,230 g\sum m = 40,230\text{ g}∑m=40,230 g.
Determine a 95% confidence interval for the population mean mass, μ\muμ, of honey in the jars.
Explain why the Central Limit Theorem was necessary for the calculation in part (b).
The apiary labels the jars as containing an average of 500 g of honey.
Using your confidence interval, evaluate the suggestion that the apiary is under-filling the jars. Justify your answer.
