Suppose claim amount for an insurance company follows a discrete distribution Pe 0.5 100 0.4 200 0.05 500 0.04 1000 0.005 10000 0.005 Find the cash values which company should hold to be able to cover claims completely with 95% and 99% confidence levels. Calculate Tail risks TVARO.01

1.A professor knows from past experience that the time for students to complete a quiz is normally distributed with mean 25 minutes and standard deviation 2 minutes. (a) If the teacher allows 26 minutes for the quiz, what percent of the students will not complete the quiz? (Round your answer to two decimal places.) %(b) Suppose that the teacher wants to allow sufficient time so that 95% of the students will complete the quiz in the allotted time. How much time should be allowed for the quiz? (Round your answer to two decimal places.)       minutes 2.Consumer Reports rated airlines and found that 84% of the flights involved in the study arrived on time (that is, within 15 minutes of scheduled arrival time). Assuming that the on-time arrival rate is representative of the entire commercial airline industry, consider a random sample of 188 flights. What is the expected number that will arrive on time? What is the standard deviation of this distribution? (Use 2 decimal places.) ?…

An investment company is promoting their mutual investment funds. Their fund specializing in the Hong Kong stock market has been consistently outperforming the Hang Seng Index over the last ten years. The company argues that such strong performance is proof of their great ability in selecting stocks for long-term investment.     Based on your understanding of the data generating process and the possible biases associated with it, provide an alternative interpretation of the statistics about fund performance.

What is the answers for b and c?

(Please do not give solution in image format thanku) Individual members of an insured group have independent claims. Aggregate payment amounts for males have mean 2 and variance 4, while payment amounts for females have mean 4 and variance 10. The premium for a group with future claims S is the expected value of S plus 2 times the standard deviation of S. If the genders of the members of a group of m members are not known, the number of males is assumed to have a binomial distribution with mean (0.4)m and variance (0.24)m. Let A be the premium for a group of 100 for which the genders of the members are not known and let B be the premium for a group of 40 males and 60 females. Determine A – B.

Acarsalespersonestimatesthefollowingprobabilities forthenumberofcarsthatshewillsellinthenextweek:Numberofcars 0 1 2 3 4 5Probability 0.10 0.20 0.35 0.16 0.12 0.07a. Find the expected number of cars that will be sold in the week.b. Find the standard deviation of the number of cars that will be sold in the week.c. The salesperson receives a salary of $250 for the week, plus an additional $300 for each car sold. Find the mean and standard deviation of her total salary for the week.d. What is the probability that the salesperson’s sal- ary for the week will be more than $1,000?