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- After an automobile is 1 year old, its rate of depreciation at any time is proportional to its value at that time. If an automobile was purchased on March 1, 2022, and its values on March 1, 2023 and March 1, 2024, were $7000 and $5800 respectively, what is its expected value on March 1, 2028?Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to $24 minutes. The 16th percentile is a phone call that lasts minutes.You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,250,000. Over the past five years, the price of land in the area has increased 7 percent per year, with an annual standard deviation of 30 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,500,000. The risk-free rate of interest is 5 percent per year, compounded continuously. How much should you charge for the option? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
- Mario's weekly poker winnings have a mean of $353 and a standard deviation of $67. Last week he won $185. How many standard deviations from the mean is that?Andrew plans to retire in 40 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. What is the probability (assuming that past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 10%? What is the probability that the mean return will be less than 5%?Exercise 6. Regression Fallacy. Historically, scores on the two midterms had a correlation of 0.48. Suppose that Jeri scored 2.1 standard deviations below the mean on the first midterm. (a) How many standard deviations [above or below?] the mean would you predict for her second midterm?
- Andrew plans to retire in 30 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. (a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 30 years will exceed 11%? (b) What is the probability that the mean return will be less than 4%?Assume time to failure density function (in months) of transplanted kidneys has a Weibull distribution with shape factor of 3 and scale of 6. Use R and answer the following questions (enter your answers with 3 decimal points):A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?
- There are two national college-entrance examinations, the scholastic aptitude test (SAT) and the American College Testing program (ACT). Scores on the SATs are approximately normal with mean 500 and standard deviation 100. Scores on the ACTs are approximately normal with mean 18 and standard deviation 6. Use the links provided for the Normal (Links to an external site.)calculator and the Inverse Normal (Links to an external site.) calculator to help complete the problems, you do not need to do any work out by hand. (instructions on how to use these calculators can be found in the week 5 star on the home page) a) What percent of all SAT scores are above 600? b) Which is the greater accomplishment, scoring 630 on the SAT or 22 on the ACT ? Explain your reasoning for your choice. c) How high a score in the SAT is needed to place in the top 2.5%.please help with this questionDetermine if the following statements are true or false. a. Jane took a sample of n = 100 observations from a population with mean and standard deviation. Mike also took a sample of n = 200 observations from the same population. Then, Mike’s sample mean will be closer to the true population mean than Jane’s sample. b. Jane took a sample of n = 100 observations from a population with mean and standard deviation. Mike also took a sample of n = 200 observations from a population with mean and standard deviation 2. Then, the sample mean from Mike’s sample is more likely to be close to the true mean than the sample mean from Jane’s sample. That is, the probability that X is between 90% and 110% of mean is higher for Mike’s sample than for Jane’s sample.
