Question

A soda machine dispenses normally distributed amounts of soda with a mean of 20 ounces and a standard deviation of 0.2 ounce. Are you more likely to randomly select one bottle with more than 21.3 ounces or are you more likely to select a sample of eight bottles with a mean amount of more than 21.3 ounces? Explain.

Answer 1

We are more likely to select a single bottle with 21.3 as compared to mean of eight bottles because for n = 8, the standard error of mean will decrease and hence, z score would be more extreme as compared to a single bottle.

z score for one bottle = (21.3 - 20)/0.2 = 6.5

z score for mean of 8 bottles = (21.3 - 20)/(0.2/) = 18.38