Consider an insurance company that sells car insurance to several thousand households in south Florida. Each policy has a return of 1% and a standard deviation of 5%. Policyholders only submit claims when they get into car accidents. Assume that car accidents are uncorrelated across policyholders. What is the standard deviation of the insurance company's returns?
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Consider an insurance company that sells car insurance to several thousand households in south Florida. Each policy has a return of 1% and a standard deviation of 5%. Policyholders only submit claims when they get into car accidents. Assume that car accidents are uncorrelated across policyholders. What is the standard deviation of the insurance company's returns?
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- Economics Consider a supplier that manufactures a product at $2 per unit and sells them to retailers at $7 per unit. The retailer sells each product to the end consumer at $10. At this retail price, market demand is normally distributed, with a mean of 1,000 and a standard deviation of 300. The supplier agrees to buy back unsold products for $b even though any leftover product at the end of sale period are worthless. a) What is the retailer's order quantity under local optimization when b=0? b) What is the optimal order quantity under global optimization? Round up to the nearest integer. Derive the optimal value of b. c) With the optimized value of b in the buyback clause, how many discs should an independent retailer order? Round up your solution to the nearest integer. d) What is the expected overstocking given the optimized value of $b? What is the expected understocking given the optimized value of $b? What is retailers' expected profit? What is the manufacturer's expected profit?Suppose a player's true batting average is Normal, with mu = .272, and standard deviation, sigma = 0.02. What is the probability that this player will have a batting average LESS THAN 0.250 on the basis of luck alone?Suppose a player's true batting average is Normal, with mu = .275, and standard deviation, sigma = 0.02. What is the probability that this player will have a batting average GREATER THAN 0.300 on the basis of luck alone?
- Use the body temperatures, in degrees Fahrenheit, listed in the accompanying table. The range of the data is 3.3°F. Use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the actual standard deviation of the data rounded to two decimal places, 0.69°F, assuming the goal is to approximate the standard deviation within 0.2°F. The estimated standard deviation is °F. (Round to two decimal places as needed.) Compare the result to the actual standard deviation. The estimated standard deviation is C the actual standard deviation. Thus, the estimated standard deviation Data table the goal. 99 98.2 97.5 98.4 99.2 98 98.7 98.5 98.1 98.1 98.5 99.3 98.7 96.7 96.5 98.7 98 97.3 98.4 98 97.7 98.3 98.9 97.1 99 97.1 98.7 98.6 99.4 97.6 97.6 97.7 97.9 99.4 98.7 99.6 97.8 97.9 99 98.3 97.7 98.7 98.2 98.7 97.6 98 97.7 98.6 98.5 98.3 97.7 99 96.3 98 98.2 96.8 97.3 97.3 97.5 98.5 97.6 97.7 97.2 97.7 98 98.8 99 98.5 98 97.8 97 97.3 99.1 98.7 98.6 98.3 98.4 99 98…On average a supermarket sells 500 litres of milk a day with a standard deviation of 50 litres. If the supermarket has 600 litres in stock at the beginning of a day, what is the probability that it will run out of milk? What is the probability that demand is between 450 and 600 litres in a day? How many litres should the supermarket stock if it wants the probability of running out to be 0.05? 4. How many should it stock if it wants the probability of running out to be 0.01?Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation 1150 S 28 % $ 8 % $ Expected Return N/A Doubled Tripled : #
- Data on nail salons throughout the city of Los Angeles finds an average price of a manicure is $22.50 with a standard deviation of $2.10. Data resembles the normal curve. About what percentage of nail services cost less than $18? + + + a 1. The z-score is 2. the corresponding area in the middle is 3. the percentage of manicures that cost less than $18 is,A risk-neutral worker can choose Low or High effort. The manager cannot observe the worker's action, but the manager can observe the realized revenue for the firm (either $300 or $500). Low Effort Cost for worker= $0 Probability Low Revenue ($300)=80% Probability High Revenue ($500)=20% High Effort Cost for worker= $40 Probability Low Revenue ($300)=40% Probability High Revenue ($500)=60% Instead of offering a flat wage, the manager is trying a new payment scheme. The manager is currently offering to the worker a payment equal to 40% of the revenue of the firm. Given this payment, the firm's expected profit will bea. A company produces lightbulbs whose life follows a normal distribution, with mean 1200 hours and standard deviation 250 hours. If we choose a lightbulb at random, what is the probability that its lifetime will be between 900 and 1300 hours? (answer in three decimal places) b. An instructor has found that the time spent by students on a particular homework assignment follows a normal distribution with mean 150 minutes and standard deviation 40 minutes. The probability is 0.8 that a randomly chosen student spends less than how many minutes on this assignment. (answer in one decimal place),
- Home prices in a particular neighborhood average $350k with a standard deviation of $30k. They are not Normally distributed. Your realtor pulls a random sample of 30 houses for you to look at. What is the probability that the average price of these 30 houses is more than $345k? (Please round your answer to 3 decimal places: ex, 0.123)RISK ANALYSIS A financial investor builds a portfolio that is worth an expected £35mil. The investor knows that his analysts can build a model to boost the potential return from the portfolio investment. The additional return has a Normal Distribution with mean £3mil and standard deviation £0.5mil. The investor wishes to sell his financial services at a price that guarantees his expected profit will be 5% of the total return from the portfolio. What should the price of his financial service be? Simulate (with a min of 200 repetitions) the average and the standard deviation of the profit the financial advisor realizes when setting the price for his services between 1% and 10% of the total expected return from the portfolio. Then discuss your findings.If the economy booms, Meyer&Co. stock will have a return of 20.8 percent. If the economy goes into a recession, the stock will have a loss of 13.1 percent. The probability of a boom is 63 percent while the probability of a recession is 37 percent. What is the standard deviation of the returns on the stock? 9.29% 12.43% 13.56% 14.61% 14.61%