Question 1 An insurance company rounds 50000 insurance premiums to the nearest dollar. Assuming that the fractional parts of the premiums are continuous and uniformly distributed between 0 and 1, compute the probability that the total amount owing will be altered by more than $60. You may use R to assist you in answering this question, but you would need to list out all working details. (15 marks) Question 2 A new drug cures 9 of 200 patients suffering from a type of cancer, for which the historical cure rate is 2%. Perform a test to check on the significance of this result, at both 5% and 1% levels of significance. Based on your conclusion, comments on the efficacy of the treatment using this new drug. (15 marks) Question 3 Men's heights are normally distributed with mean 180 cm and standard deviation 4 cm, while women's heights are normally distributed with mean 175 cm and standard deviation 3 cm. In a sample of 100 married couples, the average difference between husband's height and wife's height is 3.4 cm. By performing an appropriate test, comment on if the choice of partner in marriage is influenced by considerations of height, at 1% level of significance. Show full working details for your test. (15 marks)