. National income from manufacturing industries is to be estimated for 1999 from a sample of 6 of the 19 industry categories that reported figures early or that year. Incomes from all 19 industries are known for 1990 and the total is $674 billion. From the summary data provided, we wish to estimate the total national income from manufacturing in 1999, with bound on the error. All figures are in billions of constant dollars. Industry 1990 (x,) 1999 (y,)
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- Suppose that a new car costs $10,000 and that the annualoperating cost and resale value of the car are as shown inTable 13. If I have a new car now, determine a replacementpolicy that minimizes the net cost of owning and operatinga car for the next six years. Age of Car Resale Operating(Years) Value ($) Cost ($)1 7,000 300 (year 1)2 6,000 500 (year 2)3 4,000 800 (year 3)4 3,000 1,200 (year 4)5 2,000 1,600 (year 5)6 1,000 2,200 (year 6)A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). (a) Calculate the expected profit if the firm follows this benchmark strategy, i.e., E(L)A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). Now suppose the firm can also buy forward contracts on foreign currency to neutralize the effect of the exchange rate on profits. Assume that these provide complete hedging, but that it involves an additional cost, so that following the…
- A car rental company is developing a replacement plan for its car fleet over the next 4 years. Based on past data, they have estimated all costs associated with replacement of individual cars within this planning horizon. All costs such as purchasing, operating, maintenance, and resale, associated with the policy to buy a car in year i and sell it in year j, is denoted as c, and is estimated for the whole planning horizon (in x$1000. All replacements (buying and selling) are assumed to occur at the beginning of the indicated years, and a car must be in service for at least one year before replacement is considered. What is the least cost replacement policy?The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of thecanteen arrive at an average of 50 an hour. Suppose that management wants toevaluate the desirability of opening a second order-processing station so that twocustomers can be served simultaneously. Assume a single waiting line with the firstcustomer in line moving to the first available server.a. What is the average arrival time in minutes of customers?b. What is the average service time in minutes of the canteen?c. What is the probability that the canteen has a customer?d. What is the probability that the canteen does not have any customer?e. How long would the line be on average (average number of customers in thesystem)?f. How many people are waiting to be served on average?g. How long in minutes would it take the customer from lining up until he leaves thewaiting line?h. How long in minutes would a customer wait to be served on average?i. Find the probability that there are 7 customers in the…Suppose that you would like to create composite indexes from three stocks: stk1, stk2, stk3. Their stock prices (Pt) and total shares outstanding (Qt) from day 0 to day 1 are shown as follows: stk3 splits two-for-one in day 1. P0 Q0 P1 Q1 stk1 40 250 50 250 stk2 50 100 50 100 stk3 60 150 50 300 Which answer is the closest value to the rate of return on a price-weighted index of the three stocks? A. 20% B. 25% C. 30% D. 35%
- Two of the mathematics professors at Enormous State University are Professor A (known for easy grading) and Professor F (known for tough grading). Last semester, roughly three-fifths of Professor F's class consisted of former students of Professor A; these students apparently felt encouraged by their (utterly undeserved) high grades. (Professor F's own former students had fled in droves to Professor A's class to try to shore up their grade point averages.) At the end of the semester, as might have been predicted, all of Professor A's former students wound up with a C− or lower. The rest of the students in the class—former students of Professor F who had decided to "stick it out"—fared better, and one-fourth of them earned higher than a C−. After discovering what had befallen them, all the students who earned C− or lower got together and decided to send a delegation to the Department Chair to complain that their grade point averages had been ruined by this callous and heartless beast!…A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1pm lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapse from when the customer enters the queue until he/she reaches the teller’s window. In addition, suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 pm lunch period and data were collected at random at these branches and recorded below; No of Customers Commercial dist branch (time) Residential area branch (time) 1 – 5 3 3 6 - 10 5 6 11 - 15 8 5 16 – 20 8 3 21 - 25 4 2 Required Which of the branches has a relatively better mean waiting time? Which shop can be surer of meeting the mean waiting time at the two branches? Assuming…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…
- The cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of the canteen arrive at an average of 50 an hour. Suppose that management wants to evaluate the desirability of opening a second order-processing station so that two customers can be served simultaneously. Assume a single waiting line with the first customer in line moving to the first available server. a. What is the average arrival time in minutes of customers? b. What is the average service time in minutes of the canteen? c. What is the probability that the canteen has a customer?A candy manufacturer selects mints at random from the production line and weighs them. For one week, the day shift weighed n1 = 194 mints and the night shift weighed n2 = 162 mints. The numbers of these mints that weighed at most 21 grams was y1 = 28 for the day shift and y2 = 11 for the night shift. Let p1 and p2 denote the proportions of mints that weigh at most 21 grams for the day and night shifts, respectively. a) Give a point estimate for p1-p2 b) Find and interpret a 95% confidence interval for p1-p2 c) Can you claim a difference between difference between proportions of mints that weight at most 21g for the day and night shifts?The process for cleaning up waste in a nuclear reactor core room eliminates 85% of the waste present in the area. If there is 1.7 kg of waste in the room at the beginning of the monitoring period and 2 kg of additionalwaste are generated each week, determine a recurrence relation and initial conditions describing the amount wn, of waste in the core room at the end of week n of the monitoring period.