X O Question 1 [50 marks] O The insurance industry has faced many problems in the past 20 years. Some problems are the O decline in the popularity of life and health insurance and two decades of poor underwriting. Lately, public liability insurance has been a problem. In particular, insurance premiums for O 2001. many businesses have gone up after the terrorist attack in the United States on 11 September O Insurance companies have since bounced back in the last few years to make record profits. The O effects of poor underwriting during the 1980s and 1990s were slowly eased by positive underwriting. KPMG undertakes half-yearly surveys (to the end of June and December) of the insurance industry, and their surveys show that in the 2005-06 reporting season gross written premiums increased by 3.5% to $26.08 billion while after tax profit increased by 3.1% to a record of $3.56 billion. The 2006-07 after tax profit was another record of $3.95 billion. This was despite the Queen's Birthday weekend storms, which cost about $1.5 billion in claims, the second largest insurance loss in Australia after 1999 Sydney hailstorm that cost $1.7 billion. However, the last half of 2007 bought new challenges to the insurance industry. There were further severe storms (Western Sydney hailstorm in December and storms and the earthquake in Gisborne in the North Island of New Zealand). While no single event equalled these three in severity, continued high frequency of weather events cost the industry more than $1.15 billion (before re-insurance and tax) in 2008. The ever-widening effect of the global credit crunch and downturn in the markets has further exacerbated the situation. The result of all these factors has been an overall after-tax profit of $3.2 billion (for the insurers surveyed), a decrease ofO O Question 3 O Suppose the average cost of home and contents insurance in New Zealand is $600 per year. If home O and contents insurance sots are across New Zealand are uniformly distributed with a minimum $400, O what is probability that an individual homeowner is paying less than 500? Suppose home and contents insurance cost are normally distributed with a mean $700 and a standard deviation of $78, O What is the probability that a randomly selected household is paying between $600 and $700 for home and contents insurance? [15 marks] O HEY BIA X X Q E 66 7O O Question 4 O Suppose that 20% of all life insurance prefer purchasing insurance over the phone or by internet. Suppose a survey of 80 randomly selected customer is taken. What is the probability that 21 or more O of those selected prefer purchasing life insurance over the phone or via internet? [10 marks] O B IA X X QEE 66 * O O O O Question 2 [15 marks] Question 6 as To investifO Using the information provided, answer the following questions. O Question 2 O Suppose the average yearly cost of car insurance in Australia is $800. Since the annual insurance cost O varies by location, what probability distribution best describe the cost of car insurance in Australia? Are the data uniformly or normally distributed? If the data are normally distributed with a mean $800 O and standard deviation $100, what percentage of consumer pay more than $900? [15 marks] O B IA X X 2- O O Question 3