129. The proportion X of yearly dental claims that exceed 200 is a random variable with probability density function

 Calculate Var[X/(1 – X)]
(A) 149/900
(B) 10/7
(C) 6
(D) 8
(E) 10

130. This year, a medical insurance policyholder has probability 0.70 of having no emergency room visits, 0.85 of having no hospital stays, and 0.61 of having neither emergency room visits nor hospital stays Calculate the probability that the policyholder has at least one emergency room visit and at least one hospital stay this year. (A) 0.045 (B) 0.060 (C) 0.390 (D) 0.667 (E) 0.840

131. An insurer offers a travelers insurance policy. Losses under the policy are uniformly distributed on the interval [0, 5]. The insurer reimburses a policyholder for a loss up to a maximum of 4. Determine the cumulative distribution function, F, of the benefit that the insurer pays a policyholder who experiences exactly one loss under the policy. (A)(B)(C)(D)(E)

132. A company issues auto insurance policies. There are 900 insured individuals. Fifty-four percent of them are male. If a female is randomly selected from the 900, the probability she is over 25 years old is 0.43. There are 395 total insured individuals over 25 years old. A person under 25 years old is randomly selected. Calculate the probability that the person selected is male. (A) 0.47 (B) 0.53 (C) 0.54 (D) 0.55 (E) 0.56

133. An insurance company insures red and green cars. An actuary compiles the following data:   The actuary randomly picks a claim from all claims that exceed the deductible. Calculate the probability that the claim is on a red car. (A) 0.300 (B) 0.462 (C) 0.491 (D) 0.667 (E) 0.692

134. George and Paul play a betting game. Each chooses an integer from 1 to 20 (inclusive) at random. If the two numbers differ by more than 3, George wins the bet. Otherwise, Paul wins the bet. Calculate the probability that Paul wins the bet. (A) 0.27 (B) 0.32 (C) 0.40 (D) 0.48 (E) 0.66

135. A student takes an examination consisting of 20 true-false questions. The student knows the answer to N of the questions, which are answered correctly, and guesses the answers to the rest. The conditional probability that the student knows the answer to a question, given that the student answered it correctly, is 0.824.. Calculate N. (A) 8 (B) 10 (C) 14 (D) 16 (E) 18

136. The minimum force required to break a particular type of cable is normally distributed with mean 12,432 and standard deviation 25. A random sample of 400 cables of this type is selected. Calculate the probability that at least 349 of the selected cables will not break under a force of 12,400. (A) 0.62 (B) 0.67 (C) 0.92 (D) 0.97 (E) 1.00

137. The number of policies that an agent sells has a Poisson distribution with modes at 2 and3. K is the smallest number such that the probability of selling more than K policies is less than 25%. Calculate K. (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

138. Two fair dice are tossed. One die is red and one die is green. Calculate the probability that the sum of the numbers on the two dice is an odd number given that the number that shows on the red die is larger than the number that shows on the green die. (A) 1/4 (B) 5/12 (C) 3/7 (D) 1/2 (E) 3/5

139. In 1982 Abby’s mother scored at the 93rd percentile in the math SAT exam. In 1982 the mean score was 503 and the variance of the scores was 9604. In 2008 Abby took the math SAT and got the same numerical score as her mother had received 26 years before. In 2008 the mean score was 521 and the variance of the scores was 10,201. Math SAT scores are normally distributed and stated in multiples of ten. Calculate the percentile for Abby’s score. (A) 89th (B) 90th (C) 91st (D) 92nd (E) 93rd

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