A recent survey by a local municipality established that daily water usage by  its households is normally distributed with a mean of 220 litres and a standard deviation of 45 litres.

(a) Use standard normal z-tables to answer the following questions:

(i) What percentage of households is likely to use more than 300 litres of water per day?

(ii) What is the probability of finding a household that uses less than 100 litres of water per day?

(iii) What is the most amount of water used per day by the lowest-consuming 15% of households?

(iv) The municipality plans to implement a differential tariff policy to charge households that use more than a certain volume of water per day a higher rate per litre. If the municipality wants no more than 20% of households to pay this higher rate per litre, how much water per day must a household use before they will pay the higher rate per litre?

(b) Use the Excel function NORMDIST to solve (a)(i) and (ii).

(c) Use the Excel function NORMINV to solve (a)(iii) and (iv).