STAT 210 Final Exam | Complete Solutions (Verified)

STAT 210 Final Exam | Complete Solutions (Verified) Sampling is used heavily in manufacturing and service settings to ensure high-quality products. In which of the following areas would sampling be inappropriate? Computer assembly Custom cabinet making Cell phone manufacturing Technical support by phone An analyst studies a data set of the 2011 year-end book value per share for all companies listed on the New York Stock Exchange. This data set is best described as: timeseries data cross-sectional data neither timeseries nor cross-sectional data a combination of timeseries and cross-sectional data Thirty students at Eastside High School took the SAT on the same Saturday. Their raw scores are given next. Consider a frequency distribution of the data that groups the data in classes of 1400 up to 1600, 1600 up to 1800 , 1800 up to 2000 and so on. What percent of students scored less than 2200? 10% 20% 80% 90% Use the following data to construct a scatterplot. What type of relationship is implied? No relationship A positive relationship A negative relationship Not enough information to answer The following frequency distribution shows the frequency of the asking price, in thousands of dollars, for current homes on the market in a particular city. What percentage of houses has an asking price under $550,000? 50.5% 69.1% 89.1% 95.0% The manager at a water park constructed the following frequency distribution to summarize attendance in July and August. What of the following is the most likely attendance range? 2,000 up to 2,500 1,750 up to 2,000 1,000 up to 1,750 1,250 up to 1,750 Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. With the beginning of the next academic year, all professors will get a 2% raise. What will be the average and the standard deviation of their new salaries? $80,000 and $6,120 $81,600 and $6,000 $81,600 and $6,120 $82,000 and $6,200 The table below gives statistics relating to a hypothetical 10-year record of two portfolios. Assume other statistics relating to these portfolios are the same and the risk-free rate is 3.5%. Using the coefficient of variation and the Sharpe ratio, the fund that is preferred in terms of relative risk and return per unit of risk is:_______. Using the coefficient of variation and the Sharpe ratio, the fund that is preferred in terms of relative risk and return per unit of risk is _______. Portfolio A because it has a higher coefficient of variation and a lower Sharpe ratio. Portfolio A because it has a lower coefficient of variation and a higher Sharpe ratio. Portfolio B because it has a higher coefficient of variation and a lower Sharpe ratio. Portfolio B because it has a lower coefficient of variation and a higher Sharpe ratio. Amounts spent by a sample of 200 customers at a retail store are summarized in the following relative frequency distribution. The mean amount spent by customers is the closest to _____. $17.50 $20.00 $22.50 $50.00 Amounts spent by a sample of 50 customers at a retail store are summarized in the following relative frequency distribution. The mean amount spent by customers is the closest to_____. $0.36 $18.00 $20.00 $25.00 The following frequency distribution represents the number of hours studied per week by a sample of 50 students. The standard deviation of the number of hours studied is _____. 1.89 2.79 3.50 3.56 Automobiles traveling on a road with a posted speed limit of 65 miles per hour are checked for speed by a state police radar system. The following is a frequency distribution of speeds. The standard deviation of this distribution is the closest to _____. 5.35 6.81 9.54 10.25 The covariance between the returns of A and B is -0.112.The standard deviation of the rates of return is 0.26 for stock A and 0.81 for stock B. The correlation of the rates of return between A and B is the closest to _____. -1.88 -0.53 0.53 1.88 The covariance between the returns on two assets is negative. This occurs when... the variance of one asset has a negative linear relationship with the variance of the other asset the standard deviation of one asset has a positive linear relationship with the standard deviation of the other asset on average, the return on one asset is below its expected value and the return on the other asset is above its expected value on average, the return on one asset is below its expected value and the return on the other asset is below its expected value The director of graduate admissions is analyzing the relationship between scores in the Graduate Record Examination(GRE) and student performance in graduate school, as measured by a student's GPA. The table below shows a sample of 10 students. The covariance is _____. 53.5 51.75 57.5 58.75 Let P(AnB) = 0.3, and P(A n B^c) =0.15, and P(A^c n B) = 0.35. Compute P(A^c n B^c). 0.20 0.50 0.65 0.70 An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes's theorem, the posterior probability that the company will experience a decline is 18% 26% 44% 69% Suppose that 60% of the students do homework regularly. It is also known that 80% of students who had been doing homework regularly end up doing well in the course. Only 20% of students who had not been doing homework regularly end up doing well in the course. What is the probability that a student does well in the course? 0.080 0.480 0.560 0.857 An investor has a $100,000 portfolio of which $75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The standard deviation of the portfolio is____. 9.39(%) 14.19(%) 88.23(%)^2 201.41(%)^2 According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. What is the probability that at least one of the expectant mothers will have a Caesarean delivery? 0.0606 0.2090 0.9394 0.9742 For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. What is the probability that at least two of the customers redeem the coupon? 0.2472 0.3513 0.4015 0.7528 A bank manager estimates that an average of two customers enter the tellers' queue every five minutes. Assume that the number of customers that enter the tellers' queue is Poisson distributed. What is the probability that exactly three customers enter the queue in a randomly selected five-minute period? 0.0902 0.1804 0.2240 0.2707 According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the probability that one or more earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next year? 0.0488 0.1353 0.4878 0.9512 Suppose a baseball team has 14 players on the roster who are not members of the pitching staff. Of those 14 players, assume that three have recently taken a performance-enhancing drug. Suppose the league decides to randomly test five members of the team. What is the probability that exactly two of the tested players are found to have taken a performance-enhancing drug? 0.2308 0.2473 0.4945 0.7692 Find the z value such that P(-z ≤ Z ≤ z) = 0.95. z = -1.645 z = -1.96 z = 1.645 z = 1.96 The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car. 0.0000 0.5000 0.7580 0.2420 Let X be normally distributed with mean μ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.0606. -1.55 1. Let X be normally distributed with mean μ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736. -0.94 0.94 20.30 29.70 You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. Above what temperature must the sleeping bag be suited such that the temperature will be too cold only 5% of the time? -1.645 1.645 18.84 45.16 Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power? 0.0475 0.4525 0.9525 1.6667 The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is more than a minute? 0.2231 0.4869 0.5134 0.7769 Suppose that, on average, electricians earn approximately μ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000 dollars. What is the probability that the average salary of four randomly selected electricians is more than $50,000 but less than $60,000? 0.5899 0.7486 0.8413 0.9048 Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228? 0.0618 0.2390 0.7594 0.8212 Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. Professor Elderman offers his class of 36 a pizza party if the class average is above 80. What is the probability that he will have to deliver on his promise? 0.0228 0.3707 0.6293 0.9772 A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students who receive an A is between 0.20 and 0.35 is 0.1867 0.7766 0.8133 0.9633 The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (C). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What is the probability that between 60% and 62.5% of those surveyed are members of the labor force? 0.0243 0.1931 0.2005 0.3936 A local company makes snack-size bags of potato chips. Each day, the company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. However, due to imperfect technology, the actual amount placed in a given bag varies. Assume the amount placed in each of the 400 bags is normally distributed and has a standard deviation of 0.1 ounce. What is the probability that a sample of 40 bags has an average weight of at least 2.02 ounces? 0.0150 0.0918 0.1038 0.4207 According to the recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy. Assume 150 patients decide to get their genome sequenced. If the claim by scientists is accurate, what is the probability that fewer than 70% of the patients will get a correct diagnosis for extreme longevity? 0.1422 0.0722 0.2214 0.0207 Suppose taxi fare from Logan Airport to downtown Boston is known to be normally distributed with a standard deviation of $2.50. The last seven times John has taken a taxi from Logan to downtown Boston, the fares have been $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65. What is a 95% confidence interval for the population mean taxi fare? [$17.4571, $27.2571] [$20.5051, $24.2091] [$20.8027, $23.9115] [$21.6571, $23.0571] Given a sample mean of 12.5—drawn from a normal population, a sample of size 25, and a sample variance of 2.4—find a 99% confidence interval for the population mean. [11.7019, 13.2981] [11.1574, 13.8426] [11.6334, 13.3666] [11.7279, 13.2721] The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure, and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston. [126.2730, 539.2270] [259.7486, 405.7514]