Running head: CONTINUOUS PROBABILITY DISTRIBUTION Continuous Probability Distribution Anas F. Muqatish Mercy College 1 CONTINUOUS PROBABILITY DISTRIBUTION 2 1. Suppose the probability distribution of the lifetimes of the participants in the plan is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75? Answer: Z score for 75 = (75-68)/3.5 = 2 Thus required proportion/probability is, P(X > 75) = 1- P(X<75) = 1- P(Z<2) = 1- 0.9772 = 0.0228 2. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients die before they reach the standard retirement age of 65? Answer: Z score for 65 = (65-68)/3.5 = -0.86 Thus required proportion/probability is, P(X < 65) = P(Z< -0.86) = 0.1949 3. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants. Answer: We know, Z score = (X-mean)/SD CONTINUOUS PROBABILITY DISTRIBUTION X = mean + Z score*Sd Now for normal distribution the 86th percentile is 1.08. Thus here the required age is = (68+1.08*3.5) years = 71.78 years. 3