Assuming the appropriate probability distribution for the situation described in the preceding problem: a. Find the probability that the system will last 100,000 hours or more (twice the average lifetime). b. The system is guaranteed to last at least 5,000 hours. What percentage of production is expected to fail during the guarantee period?
> Your company prepares and distributes frozen foods. The package claims a net weight of 24.5 oz. A random sample of today’s production was weighed, and the results were summarized as follows: average = 24.41 oz, standard deviation = 0.11 oz, sample size =
> Your company is planning to market a new reading lamp and has segmented the market into three groups: avid readers, regular readers, and occasional readers. As part of a marketing survey, 400 individuals have been randomly selected from the population of
> A market survey has shown that people will spend an average of $15.48 each for your product next year, based on a sample survey of 483 people. The standard deviation of the sample was $2.52. Find the two-sided 95% confidence interval for next year’s mean
> Your bakery produces loaves of bread with “1 pound” written on the label. Here are weights of randomly sampled loaves from today’s production: 1:02,0:97,0:98,1:10,1:00,1:02 0:98,1:03,1:03,1:05,1:02,1:06 Find the 95% confidence interval for the mean weigh
> View the 989 donors in the donations database (out of 20,000 people represented on the companion site) as a random sample from a much larger population of people who would make a donation in response to the mailing. Note that the column of 989 donation a
> A random sample of eight customers was interviewed in order to find the number of computers they planned to order next year. The results were 22, 18, 24, 47, 64, 32, 45, and 35. You are interested in knowing about the larger population that these custome
> Main-course taste scores have been recorded for 48 restaurant diners on a scale from 1 to 5. The average score was 4.125, the standard error was 0.1099, and the 95% confidence interval extended from 3.904 to 4.346. Find the margin of error.
> For the ages: Answer the parts of exercise 2. Data from exercise 2: For the annual salary levels: a. Construct a cumulative distribution function. b. Find the median, quartiles, and extremes. c. Construct a box plot, and comment on its appearance. d. F
> Your agricultural firm is considering the purchase of some farmland, and an indication of the quality of the land will be helpful. A random sample of 62 selected locations planted with corn indicates an average yield of 103.6 bushels per acre, with a sta
> Draw a random sample off our firms from a population of 86 suppliers, starting with row 30, column 4 of the table of random digits.
> Draw a random sample of three account numbers from a population of 681 accounts receivable documents, starting with row 6, column 2 of the table of random digits.
> Select a random sample of four without replacement from the following metal products corporations: Gillette, Crown Cork & Seal, MASCO, Tyco Laboratories, Illinois Tool Works, McDermott, Ball, Stanley Works, Harsco, Hillenbrand Industries, Newell, Snap-on
> Select a random sample of three without replacement from the following (very small) population of firms: IBM, GM, Ford, Shell, HP, Boeing, and ITT. Use the following sequence of random digits:5887053671352339.
> You have chosen a sample of 25 supermarkets out of the 684 you have responsibility for. These 25 have been inspected, and the number of violations of company policy has been recorded. For each of the following quantities, state whether it is a statistic
> From a list of the 729 people who went on a cruise, 25 were randomly selected for interview. Of these, 21 said that they were “very happy” with the accommodations. a. What percent of the sample said that they were “very happy”? b. If you had been able to
> Based on careful examination of a sample of size 868 taken from 11,013 inventory items in a warehouse, you learn that 3.6% are not ready to be shipped. a. Find the standard error associated with this estimated percentage and indicate its meaning. b. Woul
> Consider an election poll designed so that each household has an equal chance of being selected and one registered voter is interviewed from each selected household. Analyze what would happen if single-voter households were more likely to vote Democratic
> In a study of brand recognition, out of 763 people chosen at random, 152 were unable to identify your product. a. Estimate the percentage of the population (from which this sample was taken) who would be unable to identify your product. b. Find the stand
> For the ages: Answer the parts of exercise 1. Data from exercise 1: For the annual salary levels: a. Find the average. b. Find the median. c. Construct a histogram, and give an approximate value for the mode. d. Compare these three summary measures. Wh
> A survey of 823 randomly selected adults in the United States finds that 63% support current government policies. Find the usual measure that indicates approximately how far this sample percentage is from the value that would have been found if all adult
> Find the average and the standard error for the weight of candy bars before intervention, based on the data in Table 5.4 of Chapter 5. Table 5.5.4: TABLE 5.5.4 Weight (in Ounces) for Two Samples of Candy Bars Before Before After After Intervention
> Find the average and the standard error for the strength of cotton yarn used in a weaving factory, based on the data in problem 23 of Chapter 4. Data from problem 23: Consider the strength of cotton yarn used in a weaving factory, in pounds of force at
> Find the average and the standard error for the amounts that your regular customers spent on your products last month, viewing the data from problem 2 of Chapter 4 as a sample of customer orders. Data from problem 2: Table 4.3.1 provides a list of the
> A random sample of 50 recent patient records at a clinic shows that the average billing per visit was $53.01 and the standard deviation was $16.48. a.* Find the standard error of the average and interpret it. b. You feel that this standard error is too l
> Find the standard error of the average for the following data set representing quality of agricultural produce: 16:7,17:9,23:5,13:8,15:9,15:2,12:9,15:7
> The sample average age is 69.8 and the sample standard deviation is 9.2, based on a sample of 200 individuals in a retirement community. Your friend claims that “the sample average is approximately 9.2 away from the population mean.” Is your friend corre
> Which of the following samples is likely to be the most representative of the population of all employees at IBM? a. The 10 oldest and most experienced researchers at the Thomas J. Watson Research Center. b. A random sample of 10 computer repair speciali
> Your customers’ average order size is $2,601, with a standard deviation of $1,275. You are wondering what would happen if exactly 45 typical customers independently placed orders tomorrow. a.* Find the mean of tomorrow’s total orders. b.* Find the standa
> A typical incoming telephone call to your catalog sales force results in a mean order of $28.63 with a standard deviation of $13.91. You may assume that orders are received independently of one another. a. Based only on this information, can you find the
> For the genders: a. Summarize by finding the percent of each category. b. Find the mode. What does this tell you?
> You have analyzed a project using four scenarios, with the results shown in Table 8.6.1. Suppose you actually have 40 projects just like this one and they pay off independently of one another. Find the probability that your average profit per project wil
> The population mean is$65 and the population standard deviation is $30. Find the probability that the average of 35 randomly selected transactions is between $55 and $60. You may assume that the population is approximately normally distributed.
> A farmer has five identical cornfields, each of which independently produces a normally distributed harvest with a mean of 80,000 bushels and a standard deviation of 15,000 bushels. Find the probability that the average harvest for the five fields will e
> Breakfast cereal is packed into packages labeled “net weight 20 ounces, packed by weight not by volume; some settling may occur during shipment.” However, weights of individual packages are not really all exactly equal to 20 oz—although they are close, t
> Which of the following samples is likely to be the most representative of the population of all registered voters in the United States? a. A sample of 200 people at a Denver shopping mall. b. A sample of 200 of your friends and their friends. c. A sample
> You have a factory with 40 production machines that are essentially identical, each producing at a mean daily rate of 90 products with a standard deviation of 35. You may assume that they produce independently of one another. Consider the random variable
> You have interviewed 369 people out of a population of 30,916 and found that 51.8% expect to vote for the challenger in the upcoming election. Find the standard error of this estimate.
> Deposits have a mean of $125 and a standard deviation of $36. Find the standard deviation of the average amount of 12 randomly selected deposits.
> You have estimated the inventory value of your competition as $384,000 but later learn that the true inventory value was $416,000. Find the estimation error.
> You have eight machines operating independently. The mean production rate for each machine is 20.3 tons/day, and the standard deviation is 1.4 tons/day. Approximately how much uncertainty is there in the average daily production for the eight machines? P
> For the annual salary levels: a. Construct a cumulative distribution function. b. Find the median, quartiles, and extremes. c. Construct a box plot, and comment on its appearance. d. Find the 10th percentile and the 90th percentile. e. What is the percen
> The population mean productivity is 35, the population standard deviation is 10, and the sample size is 15. Find the standard deviation of the total amount represented by a random sample.
> The mean account balance is $500 and the standard deviationis$120foralargepopulation of bank accounts. Find the standard deviation of the average balance of groups of eight accounts (chosen independently of one another and with equal probabilities of sel
> Draw a random sample of eight invoices from a population of 500 overdue billings, starting with row 17, column 5 of the table of random digits.
> Draw a random sample of five contracts from a population of 362 recent contracts with cost overruns, starting with row 13, column 5 of the table of random digits.
> You are planning to invest in a new high-tech company, and figure your rate of return over the coming year as in Table 7.6.4 (where 100% says that you doubled your money, 50% says you lost half, etc.). a. Find the mean rate of return and explain what it
> You work for the loan department of a large bank. You know that one of your customers has been having trouble with the recession and may not be able to make the loan payment that is due next week. You believe there is a 60% chance that the payment of $50
> A new project has an uncertain cash flow. A group meeting has resulted in a consensus that a reasonable way to view the possible risks and rewards is to say that the project will pay $50,000 with probability 0.2, will pay $100,000 with probability 0.3, w
> Compare the “probability of being within one standard deviation of the mean” for the exponential and normal distributions.
> In the situation described in the previous problem, a customer has just arrived. a. Find the probability that the time until the arrival of the next customer is less than 3 minutes. b. Find the probability that the time until the arrival of the next cust
> For the annual salary levels: a. Find the average. b. Find the median. c. Construct a histogram, and give an approximate value for the mode. d. Compare these three summary measures. What do they tell you about typical salaries in this administrative divi
> Customers arrive at random times, with an exponential distribution for the time between arrivals. Currently the mean time between customers is 6.34 minutes. a. Since the last customer arrived, 3 minutes have gone by. Find the mean time until the next cus
> On a typical day, your clothing store takes care of 2.6 “special customers” on average. These customers are taken directly to a special room in the back, are assigned a full-time server, are given tea (or espresso) and scones, and have clothes brought to
> On a given day, assume that there is a 30% chance you will receive no orders, a 50% chance you will receive one order, a 15%chance of two orders, and a5% chance of three orders. Find the expected number of orders and the variability in the number of orde
> If tomorrow is a typical day, your human resources division will expect to receive resumes from 175 job applicants. You may assume that applicants act independently of one another. a. What is the name of the probability distribution of the number of resu
> You expect a mean of 1,671 warranty repairs next month, with the actual outcome following a Poisson distribution. a. Find the standard deviation of the number of such repairs. b. Find the probability of more than 1,700 such repairs.
> You have just sent out a test mailing of a catalog to 1,000 people randomly selected from a database of 12,320 addresses. You will go ahead with the mass mailing to the remaining 11,320 addresses provided you receive orders from 2.7% or more from the tes
> Suppose 17% of the items in a large warehouse are defective. You have chosen a random sample of 350 items to examine in detail. Find the probability that more than 20% of the sample is defective.
> Assume that if you were to interview the entire population of Detroit, exactly 18.6% would say that they are ready to buy your product. You plan to interview a representative random sample of 250 people. Find the probability that your observed sample per
> Reconsider the previous problem and answer each part, but assume that 1,000 people will vote. (The probability for each one remains unchanged.) Data from Problem 32: A union strike vote is scheduled tomorrow, and it looks close. Assume that the number
> A union strike vote is scheduled tomorrow, and it looks close. Assume that the number of votes to strike follows a binomial distribution. You expect 300 people to vote, and you have projected a probability of 0.53 that a typical individual will vote to s
> For the training level: Answer the parts of exercise 3. Data from exercise 3: For the genders: a. Summarize by finding the percent of each category. b. Find the mode. What does this tell you?
> What would you recommend that Harris and McRorie do to prepare for their presentation this afternoon?
> A new project will be declared “successful” if you achieve a market share of 10% or more in the next 2 years. Your marketing department has considered all possibilities and decided that it expects the product to attain a market share of 12% in this time.
> An investment will pay $105 with probability 0.7, and $125 with probability 0.3. Find the risk (as measured by standard deviation) for this investment.
> Although you do not know the exact total amount of payments you will receive next month, based on past experience you believe it will be approximately $2,500 more or less than $13,000, and will follow a normal distribution. Find the probability that you
> Assume that electronic microchip operating speeds are normally distributed with a mean of 2.5 GHz and a standard deviation of 0.4 GHz. What percentage of your production would you expect to be “superchips” with operating speeds of 3 GHz or more?
> You are a farmer about to harvest your crop. To describe the uncertainty in the size of the harvest, you feel that it may be described as a normal distribution with a mean value of 80,000 bushels and a standard deviation of 2,500 bushels. Find the probab
> The amount of ore (in tons) in a segment of a mine is assumed to follow a normal distribution with mean 185 and standard deviation 40. Find the probability that the amount of ore is less than 175 tons.
> Based on recent experience, you expect this Saturday’s total receipts to have a mean of $2,353.25 and a standard deviation of $291.63 and to be normally distributed. a. Find the probability of a typical Saturday, defined as total receipts between $2,000
> Assume that the stock market closed at 13,246 points today. Tomorrow you expect the market to rise a mean of four points, with a standard deviation of 115 points. Assume a normal distribution. a. Find the probability that the stock market goes down tomor
> The quality control section of a purchasing contract for valves specifies that the diameter must be between 2.53 and 2.57 cm. Assume that the production equipment is set so that the mean diameter is 2.56 cm and the standard deviation is 0.01 cm. What per
> Under usual conditions, a distillation unit in a refinery can process a mean of 135,000 barrels per day of crude petroleum, with a standard deviation of 6,000 barrels per day. You may assume a normal distribution. a. Find the probability that more than 1
> For the experience variable: Answer the parts of exercise 2. Data from exercise 2: For the annual salary levels: a. Construct a cumulative distribution function. b. Find the median, quartiles, and extremes. c. Construct a box plot, and comment on its a
> Find the probability that you will see moderate improvement in productivity, meaning an increase in productivity between 6 and 13. You may assume that the productivity increase follows a normal distribution with a mean of 10 and a standard deviation of 7
> Suppose that the number of hits on your company’s website, from noon to 01:00 pm on a typical weekday, follows a normal distribution (approximately) with a mean of 190 and a standard deviation of 24. a. Find the probability that the number of hits is mor
> You are planning to make sales calls at eight firms today. As a rough approximation, you figure that each call has a 20% chance of resulting in a sale and that firms make their buying decisions without consulting each other. Find the probability of havin
> You have just performed a survey interviewing 358 randomly selected people. You found that 94 of them are interested in possibly purchasing a new cable TV service. How much uncertainty is there in this number “94” as compared to the average number you wo
> Repeat the previous problem, but now assume that 85% are in favor in the population. Is the uncertainty larger or smaller than when 50% was assumed? Why? Data from Problem 14: An election coming up next week promises to be very close. In fact, assume t
> An election coming up next week promises to be very close. In fact, assume that 50% are in favor and 50% are against. Suppose you conduct a poll of 791 randomly selected likely voters. Approximately how different will the percent in favor (from the poll)
> A company is conducting a survey of 235 people to measure the level of interest in a new product. Assume that the probability of a randomly selected person’s being “very interested” is 0.88 and that people are selected independently of one another. a. Fi
> Your company is planning to market a new reading lamp and has segmented the market into three groups—avid readers, regular readers, and occasional readers—and currently assumes that 25% of avid readers, 15% of regular readers, and 10% of occasional reade
> Two divisions are cooperating in the production of a communications satellite. In order for the launch to be on time, both divisions must meet the deadline. You believe that each has an 83% chance of meeting the deadline. Assuming the two divisions work
> As part of a project to determine the reliability of construction materials, 100 samples were subject to a test simulating 5 years of constant use. Of these, 11 samples showed unacceptable breakage. Find the relative frequency of the event “unacceptable
> For the experience variable: Answer the parts of exercise 1. Data from exercise 1: For the annual salary levels: a. Find the average. b. Find the median. c. Construct a histogram, and give an approximate value for the mode. d. Compare these three summa
> You are responsible for a staff of 32 out of the 118 workers in a rug-weaving factory. Next Monday a representative will be chosen from these 118 workers. Assume that the representative is chosen at random, without regard to whether he or she works for y
> You are a contestant on a TV game show with five doors. There is just one prize behind one door, randomly selected. After you choose, the hosts deliberately open three doors (other than your choice) that do not have the prize. You have the opportunity to
> The probability of getting a patent is 0.6. If you get the patent, the conditional probability of being profitable is 0.9. However, given that you do not get the patent, the conditional probability of being profitable is only 0.3. Find the probability of
> Of the 925 tires your factory just produced, 17 are defective. a. Find the probability that a randomly selected tire is defective. b. Find the probability that a randomly selected tire is not defective. c. What kind of probability numbers are these?
> You feel that the schedule is reasonable provided the new manager can be hired in time, but the situation is risky regardless. You figure there is a 70% chance of hiring the new manager in time. If the new manager is hired in time, the chances for succes
> You have determined that 2.1% of the CDs that your factory manufactures are effective due to a problem with materials and that 1.3% are defective due to human error. Assuming that these are independent events, find the probability that a CD will have at
> Your production line has an automatic scanner to detect defects. In recent production, 2% of items have been defective. Given that an item is defective, the scanner has a 90% chance of identifying it as defective. Of the non defective items, the scanner
> Of your customers, 24% have high income, 17% are well educated. Furthermore, 12% both have high income and are well educated. What percentage of the well-educated customers has high income? What does this tell you about a marketing effort that is current
> You have followed up on people who received your catalog mailing. You found that 4% ordered the hat and 6% ordered the mittens. Given that they ordered the hat, 55% also ordered the mittens. a. What percentage ordered both items? b. What percentage order
> The probability that the project succeeds in New York is 0.6, the probability that it succeeds in Chicago is0.7,and the probability that it succeeds in both markets is 0.55. Find the conditional probability that it succeeds in Chicago given that it succe
> For the salary numbers: a. Construct a histogram. b. Describe the shape of the distribution. c. Summarize the distribution in general terms by giving the smallest salary and the largest salary.
> Suppose 35.0% of employees are staff scientists, 26.0% are senior employees, and 9.1% are both. Are “staff scientist” and “senior employee” independent events?
> You just learned good news: A prototype of the new product was completed ahead of schedule and it works better than expected. Would you expect “the conditional probability that this product will be successful given the good news” to be larger than, small
> Your group has been analyzing quality control problems. Suppose that the probability of a defective shape is 0.03, the probability of a defective paint job is 0.06, and that these events are independent. a. Find the probability of defective shape and def
> All 18 people in a department have just received across the- board pay raises of 3%. What has happened to a. The average salary for the department? b. The standard deviation of salaries? c. The range in salaries? d. The coefficient of variation of salari
