1. A fund is established for the benefit of 500 workers all age 35 with independent future life- times. When they reach age 65, the fund will be dissolved and distributed to the survivors. The fund will earn interest at a rate of 5% per year. The initial fund balance, F, is determined so that the probability that the fund will pay at least 5000 to each survivor is 90%, using the normal approximation. Mortality follows the Standard Ultimate Life Table. Calculate F. (Round your answer to a multiple of 1,000.) (A) 457,000 (B) 482,000 (C) 507,000 (D) 532,000 (E) 557,000
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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