Longer exercises Exercise 3.8 A group of 100 000 independent lives, each aged 65, purchases one-year term insurance. At the start, 20% of the group are preferred lives, with 965 = 0.002 and 80% of the group are normal lives, with 965 = 0.009. = (a) Calculate the standard deviation of the number of survivors at the end of the year. (b) Calculate the proportion of preferred lives expected in the survivor group. . () Using a normal approximation, without continuity correction, calculate the 90th percentile of the number of survivors at the end of the year. Longer exercises Exercise 3.8 A group of 100 000 independent lives, each aged 65, purchases one-year term insurance. At the start, 20% of the group are preferred lives, with 965 = 0.002 and 80% of the group are normal lives, with 965 = 0.009. = (a) Calculate the standard deviation of the number of survivors at the end of the year. (b) Calculate the proportion of preferred lives expected in the survivor group. . () Using a normal approximation, without continuity correction, calculate the 90th percentile of the number of survivors at the end of the year