The Australian Bureau of Statistics reveals that the average annual expenditure of Australian households on food and drinks is $13,260. Assume that the annual expenditure on food and drink of Australian households is normally distributed and that the standard deviation is $1780.

i. What is the probability that a randomly selected Australian household spends more than $12,000 per year on food and drinks?

ii. What is annual expenditure of Australian households on food and drinks in the lower 20% of the above normal distribution?

iii. If 30 Australian households are randomly selected, what is the probability that the sample mean annual expenditure will lie between $13,000 and $13,800?