Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2009
Homework 5: Normal Distribution and CLT Due: 12/8/2009
Note : You need the standard normal distribution table (Z table) to nish the homework. . If for a certain normal random variable X , P (X < 500) = 0.5 and P (X > 650) = 1. 2. 0.0227, nd the standard deviation of X .
Normal Normal . There are two independent random variables: W and X , both normally distributed with the same mean. The variances of W and X are 4 and 12 respectively. What is P (|W − X | < 1)?
Normal 3. . Two instruments are used to measure the height, h, of a tower. The error made by the less accurate instrument is normally distributed with mean 0 and standard deviation 0.0056h. The error made by the more accurate instrument is normally distributed with mean 0 and standard deviation 0.0044h. Assuming the two measurements are independent random variables, what is the probability that their average value is within 0.005h of the height of the tower? . A charity receives 2025 contributions. Contributions are assumed to be independent and identically distributed with mean 3125 and standard deviation 250. Calculate the approximate 90th percentile for the distribution of the total contributions received.
CLT, sum 4. 5. . An insurance company issues 1250 vision care insurance policies. The number of claims led by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2. Assume the numbers of claims led by distinct policyholders are independent of one another. What is the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?
CLT, sum of Poisson 1 ...
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