G8 X V A H M N Q R S U V W X Y Z AA AB AC Normal Distribution 2 A company is examining its pension fund and pays for an actuarial study of its employees. The actuary states that the life spans of the employees will be normally distributed , 3 with an average life expectancy of 72 and a standard deviation of 5 years. Employees are selected randomly from the company. What is the probability: H = 72 0 = 5 8 (a) An employee will live less than 65 years? 9 10 11 (b) An employee will live more than 95 years? 12 13 14 (c) An employee will live between 75 and 85 year? 15 16 17 (d) How old must an employee be to be in the top 5% of long living employees? 18 19 20 (e) What is the oldest age for the shortest living 10% of employees? 21 22 23 (f) The middle 80% of employee live between what two ages? 24 Between and 25 26 (g) Recent studies have suggested that advances in healthcare may increase the lifespan of employees. How much would the average life expectancy need to rise in order for 70% of people to live to age 75 or above? 27 2 28 x 29 LL 30