Question 1 (SS-2012) (2-2013) a) State three properties of a normal distribution. b) Suppose personal daily water usage in Darwin City is normally distributed, with a mean of 18 litres and a standard deviation of 6 litres. i. What percentage of the population uses between 10 and 20 litres? ii. What is the probability that a person uses less than 10 litres? iii. If the local government wants to give a tax rebate to the 20% of the population that use the least amount of water. What should the government use as the maximum water limit for a person to qualify for a tax rebate? iv. Suppose the government's proposed tax rebate causes a shift in the average water use from 18 litres to 14 litres per person per day, but causes no shift in the standard deviation. What limit should be set on water use if 20% of the population is to receive a tax rebate? Question 2 (SS-2012) (2-2013) Records show that the average farm size in a particular region has increased over the last 70 years. This trend might be explained, in part, by the inability of small farms to compete with the prices and costs of large-scale operations and to produce a level of income necessary to support the farmers' desired standard of living. An agribusiness researcher believes the average size of farms has continued to increase since 2007 from a mean of 471 hectares. To test this, a random sample of 23 farms was selected from official government sources and their sizes recorded. The sample yielded a mean farm size of 498.78 hectares and a standard deviation of 46.94 hectares. Test the hypothesis, using either the p-value approach or the classical approach, at the 0.05 level of significance. a