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- Suppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…1. Zombies have appeared in Chicago and every day, each zombie produces 3 new zombies. Suppose that initially there is only one zombie, how many zombies will there be in 7 days? 2. In a rabbit population, each pair produces 2.2 offspring every year (i.e. 1.1 per capita) and the adults have a 0.9 annual death rate after reproduction (and assume the whole population is paired up into mating pairs.) If initially there are 55 rabbits, predict how many there will be in 5 years (rounded to the nearest integer). 3. Consider the same rabbit population, but now a python that lives nearby eats exactly 1 rabbit a month. If initially there are 55 rabbits, how many do you predict will be in 10 years?We wish to demonstrate that the average time to graduate from school is afected by the students who have taken AP calculus in hgh school. Specially, we wish to demonstrate the students who have taken AP calculus in high school graduate an average of more than .25 years sooner than students who have not taken AP calculus in high school. If we let μ1 denote the average time to graduate for students who have not taken AP calculus and μ2 dentoe the average time to graduate for students who have taken AP calculus, what is the apropriate null hypothesis
- A consumer is given the chance to buy a baseball card for $1, but hedeclines the trade. If the consumer is now given the baseball card, willhe be willing to sell it for $1? Standard consumer theory suggests yes, butbehavioral economists have found that “ownership” tends to increase thevalue of goods to consumers. That is, the consumer may hold out for someamount more than $1 (for example, $1.20) when selling the card, eventhough he was willing to pay only some amount less than $1 (for example,$0.88) when buying it. Behavioral economists call this phenomenon the“endowment effect.” John List investigated the endowment effect in a randomized experiment involving sports memorabilia traders at a sports-card show. Traders were randomly given one of two sports collectibles, say good A or good B, that had approximately equal market value.1 Those receiving good A were then given the option of trading good A for good B with the experimenter; those receiving good B were given the option of…An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns.(x, y)= What is the optimal profit?$An investor has decided to commit no more than $80,000 to the purchase of the common stocks of two companies, Company A and Company B. He has also estimated that there is a chance of at most a 1% capital loss on his investment in Company A and a chance of at most a 4% loss on his investment in Company B, and he has decided that these losses should not exceed $2000. On the other hand, he expects to make a(n) 15% profit from his investment in Company A and a(n) 18% profit from his investment in Company B. Determine how much he should invest in the stock of each company (x dollars in Company A and y dollars in Company B) in order to maximize his investment returns. What are the (x,y) values? What is the optimal profit?
- Find the sum from k=1 to infinity of: [5/(3k+1)] using the limit comparison test.4. The lifetime, in years, of a type of small electric motor operating under adverse conditions is T ~Γ(6, 3.6). Whenever the motor fails, it is replaced with another of the same type. Find theprobability that fewer than 6 motors fail within one year.Find the interval of convergence for ∑∞ n=2 (x^n)/((n^2)(3^n))