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) be from the 50% in the population you are trying to estimate?
> 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.
> 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 5,0
> 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
> 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
> Compute the standard deviation of the data from Table 4.3.1 of Chapter 4 to find the variability in spending levels from one regular customer to another for last month. Write a paragraph summarizing these differences. Table 4.3.1: TABLE 4.3.1 Last
> Summarize the variability in the cost of a traditional funeral service using the standard deviation, based on the data in Table 3.8.10 of Chapter 3. Table 3.8.10: TABLE 3.8.10 Cost of Traditional Funeral Service Funeral Home Cost ($) Bleitz $2,180
> Using the data from Table 3.8.2 in Chapter 3, find the standard deviation and range to summarize the typical variability (or uncertainty) of the market response to stock buyback announcements. Table3.8.2: TABLE 3.8.2 Market Response to Stock Buybac
> Consider the running time of movies from Table 4.3.10 in Chapter 4. a. Find the standard deviation. What does this tell you about these movie times? b. Find the range. What does this tell you about these movie times? c. How many standard deviations from
> Find the standard deviation of the VAT taxes from Table 4.3.2 in Chapter 4. What does this tell you about international taxation practices from one country to another? Table 4.3.2: TABLE 4.3.2 Value-Added Tax Rates by Country Country Standard VAT R
> For the preceding problem, compare the coefficient of variation before and after the sales goal adjustment. Why does it change (or not change) in this way?
> For the salary numbers, separated according to gender: a. Construct a histogram for just the males. b. Construct a histogram for just the females using the same scale as in part a to facilitate comparison of male and female salaries. c. Compare these two
> You are sales manager for a regional division of a beverage company. The sales goals for your representatives have an average of $768,000 with a standard deviation of $240,000. You have been instructed to raise the sales goalofeachrepresentativeby$85,000
> For the previous problem, compare the coefficient of variation before and after the price increase. Why does it change (or not change) in this way? Data from Problem 28: Your costs had been forecast as having an average of $138,000 with a standard devi
> Your costs had been forecast as having an average of $138,000 with a standard deviation of $35,000. You have just learned that your suppliers are raising prices by 4% across the board. Now what are the average and standard deviation of your costs?
> Airline ticket prices are generally optimized for the airline’s benefit, not for the consumer’s benefit. On July 8, 2010, at the online travel agency website http:// www.expedia.com, the following airfares were proposed for round trip travel from Seattle
> Consider the dollar value (in thousands) of gifts returned to each of your department stores after the holiday season (Table 5.5.9). a. Compute the sample standard deviation. b. Interpret the standard deviation in a paragraph discussing the variation fro
> Consider the average price of a hotel room in 21 U.S. cities (Table 5.5.8) for the first half of 2015. a. Find the average price of a major-city hotel room in the United States, based on this data set. b. Find the sample standard deviation of these price
> Here are weights of recently produced sinks: 20.8, 20.9, 19.5, 20.8, 20.0, 19.8, 20.1, 20.5, 19.8, 20.3, 20.0, 19.7, 20.3, 19.5, 20.2, 20.2, 19.5, 20.5 Find the usual summary measure that tells approximately how far from average these weights are.
> Consider the percentage change in the value of the dollar with respect to Asia-Pacific currencies, year-to-date as of mid-October 2015 (Table 5.5.7). a. Find the standard deviation of these percentages. b. Interpret this standard deviation. In particular
> Consider interest rates on accounts at a sample of local banks: 3.00%, 4.50%, 4.90%, 3.50%, 4.75%, 3.50%, 3.50%, 4.25%, 3.75%, 4.00% a. Find the standard deviation of these interest rates. b. What does this standard deviation tell you about banks in this
> Using the data from Table 2.6.8 of Chapter 2 for daily values for the Dow Jones Industrial Average: a. Find the standard deviation of the net change. b. Find the range of net change. c. Find the standard deviation of the percent change. d. Find the range
> For the experience numbers: a. Construct a histogram. b. Describe the shape of the distribution. c. Summarize the distribution in general terms.
> Summarize the variability in admission prices for the theme parks shown in Table 5.5.6 by reporting the standard deviation, the range, and the coefficient of variation. Table 5.5.6: TABLE 5.5.6 Theme Park Admission Prices Theme Park Admission Price
> Using the data set from the previous problem concerning the ages and maintenance costs of five similar printing presses: a. Calculate the average maintenance cost of the presses. b. Calculate the standard deviation of the maintenance costs of the presses
> Consider the ages (in years) and maintenance costs (in thousands of dollars per year) for five similar printing presses (Table 5.5.12). a. Calculate the average age of the presses. b. Calculate the standard deviation of the ages of the presses. c. Calcul
> The performance claimed by mutual funds is often considerably better than what you would experience if you actually put your money on the line. Table 5.5.11 shows the annual return for internationally diversified bond funds both before adjustment and aft
> Your firm’s total advertising budget has been set for the year. You (as marketing manager) expect to spend about $1,500,000 on TV commercials, with an uncertainty of $200,000 as the standard deviation. Your advertising agency collects a fee of 15% of thi
> Find the amount of variability in the 5-year percent change in housing prices for U.S. regions using the data from Table 4.3.5 of Chapter 4. Table 4.3.5: TABLE 4.3.5 Percent Change in Housing Values over Five Years for U.S. Regions Percent Percent
> Active consumers make up 13.6% of the market and spend an average of $16.23 per month on your product. Passive consumers make up 23.8% of the market and spend $9.85. The remaining consumers have average spending of $14.77. Find the average spending for a
> Your firm has the following securities outstanding: common stock (market value $4,500,000; investors demand 17% annual rate of return), preferred stock (market value $1,700,000; current annual yield is 13%), and 20-year bonds (market value $2,200,000; cu
> Some people who work at your company would like to visually compare the income distributions of people who buy various products in order to better understand customer selections. For each of 16 products, a list of incomes of representative customers (who
> Summarize prices of funeral services using the average and median, based on the data in Table 3.8.10 of Chapter 3. Table 3.8.10: TABLE 3.8.10 Cost of Traditional Funeral Service Funeral Home Cost ($) Bleitz $2,180 Bonney-Watson 2,250 Butterworth's
> For the age numbers: a. Construct a histogram. b. Describe the shape of the distribution. c. Summarize the distribution in general terms.
> Your factory’s inventory level was measured 12 times last year, with the results shown below. Find the average inventory level during the year. 313, 891, 153, 387, 584, 162, 742, 684, 277, 271, 285, 845
> A mail-order sales company sent its new catalog initially to a representative sample of 10,000 people from its mailing list and received orders totaling $36,851. a. Find the average dollar amount ordered per person in this initial mailing. b. What total
