A group of 1000 employees in a pension plan is subject to three decrements, namely retirement, death, and termination. The probabilities of these decrements are as follows: Decrement Retirement Death Termination Probability 0.002 0.022 0.222 You are to simulate the number of the three decrements in the following order: retirement, death, and termination. Use the following random numbers from the uniform distribution on [0,1]. 0.1230 0.5000 0.7910 (a) Using a normal approximation to the binomial distribution, determine the number of terminations. (9 marks) (b) Outline the steps used to determine the number of terminations without using a normal approximation. (3 marks) (c) Compare and comment on the approaches used in parts (a) and (b). (3 marks) A group of 1000 employees in a pension plan is subject to three decrements, namely retirement, death, and termination. The probabilities of these decrements are as follows: Decrement Retirement Death Termination Probability 0.002 0.022 0.222 You are to simulate the number of the three decrements in the following order: retirement, death, and termination. Use the following random numbers from the uniform distribution on [0,1]. 0.1230 0.5000 0.7910 (a) Using a normal approximation to the binomial distribution, determine the number of terminations. (9 marks) (b) Outline the steps used to determine the number of terminations without using a normal approximation. (3 marks) (c) Compare and comment on the approaches used in parts (a) and (b)