(3) An insurance agency sells automobile insurance policies. Suppose claims on the policies are approximately Normal...
Claims filed under auto insurance policies follow a normal distribution with mean 19,400 and standard deviation 5,000. What is the probability that the average of 25 randomly selected claims exceeds 20,000?
An insurance company has 10,000 outstanding fire policies. For each policy, there is an expected claim of $100 with a standard deviation of $400. The individual claims are independent random variables. What is the probability that the total of all claims exceeds $1,100,000.
An insurance salesperson sells an average of 3 life insurance policies per week. Suppose insurance policies sales occur according to a Poisson distribution. a) What is the probability they will sell 3 or more policies in four weeks? b) What is the expected value of policies sold in four weeks? c) What is the variance in the expected number of policies sold?
The Mountain States Office of State Farm Insurance Company reports that approximately 73% of all automobile damage liability claims were made by people under 25 years of age. A random sample of twelve automobile insurance liability claims is under study. (a) Make a histogram showing the probability that r = 0 to 12 claims are made by people under 25 years of age. (b) Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal...
The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows. Payment ($) Probability 0 0.82 500 0.05 1000 0.04 3000 0.04 5000 0.03 8000 0.01 10000 0.01 a. Use the expected collision payment to determine the collision insurance premium that would enable the company to break even. Answer: $ b. The insurance company charges an annual rate of $595 for the collision coverage. What is the expected value of the collision policy for...
Answer questions 23 and 24 based on the following: The mean annual cost of automobile insurance is $939. The standard deviation is $300. You have been asked to compute the probability that a simple random sample of automobile insurance policies of size 100 will have a sample mean within $30 of the population mean. 23. Compute the standard deviation of the population. (a) $300 (b) $3 (c) $1.73 (d) $5.48 (e) $30 24. Compute the probability that a simple random...
An insurance company has issued 100 policies. The number of claims filed under each policy follows a Poisson distribution with a mean 2. Assuming that the claims filed by each policyholder are independent of each other, what is the approximate probability that more than 220 claims will be filed by the group of policyholders? B) 0.159 A) 0.079 C) 0.444 D) 0.556 E) 0.921 Question 2-20 An actuary is studying claim patterns in an insurer's book of business. He compiles...
An automobile insurer has found that repair claims are Normally distributed with a mean of $890 and a standard deviation of $850. (a) Find the probability that a single claim, chosen at random, will be less than $840. ANSWER: (b) Now suppose that the next 100 claims can be regarded as a random sample from the long-run claims process. Find the probability that the average x¯ of the 100 claims is smaller than $840. ANSWER: (c) If a sample larger...
An automobile insurer has found that repair claims are Normally distributed with a mean of $580 and a standard deviation of $530. (a) Find the probability that a single claim, chosen at random, will be less than $560. ANSWER: (b) Now suppose that the next 100 claims can be regarded as a random sample from the long-run claims process. Find the probability that the average x¯ of the 100 claims is smaller than $560. ANSWER: (c) If a sample larger...