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Understanding Business Statistics 1st edition Stacey Jones, Tim Bergquist, Ned Freed - Solutions
For the experiment described in Exercise 66, use the binomial table at the end of the text to confirm the probabilities you produced.
According to the overnight television ratings, 45% of households in the country watched the latest episode of Parkinson’s Law on Tuesday night. If this is true and you survey 30 randomly selected households, how likely is it that a. Exactly 17 of the households in your survey watched the show? b.
Use the binomial table to produce the following binomial probabilities:a. P(x = 4), where n = 10, p = .3b. P(x = 8), where n = 20, p = .6c. P(x < 12), where n = 15, p = .7d. P(7 < x < 10), where n = 20, p = .5e. P(14 < x < 16), where n = 30, p = .6
According to recent estimates, the likelihood that an individual who earns less than $200,000 will be audited by the Internal Revenue Service is 1%; the chance that an individual making $200,000 to $1 million will be audited is put at 2.7%; and the chance that a person making over $1 million will
According to a recent study by the National Highway Traffic Safety Administration (NHTSA), the helmet usage rate for motorcyclists in the US was 55%. If this is the case and you select 15 cyclists at random, how likely is it thata. Exactly 12 of them will be helmet users?b. No more than nine of
In a recent assessment test given by the Department of Education, approximately 55% of high school seniors did not show even “basic knowledge” of American history. In fact, a substantial number of them didn’t know which side won the American Civil War. If this 55% figure is accurate, how
NASA is planning a deep space probe involving extensive scientific experimentation. The guidance system for the space vehicle is obviously critical. The system is comprised of six independent components, each of which must work as engineered in order for the overall system to function properly. If
According to the US Food and Drug Administration, the approval rate for new drug applications over the last decade is 80%. Assuming that this same rate holds in the future, if twenty new drug applications are submitted this year, how likely is it that a. Exactly 16 will be approved. b. No more than
Trenton Engineering has assigned seven engineers to work independently on a new product design. It is estimated that each engineer has a 65% chance of developing a design that is acceptable. How likely is it that Trenton ends up with a. no acceptable designs? b. at least three acceptable
You are about to take a test consisting of 20 True-False questions (a test for which you haven’t studied a lick). Your plan is merely to guess randomly on each answer. a. A passing grade on the test is 60%. Given your “pure guess” strategy, how likely is it that you will pass the test? b. To
You now discover that part c of Exercise 75 was just a bad dream. The exam is tomorrow and it will definitely be True-False. Sobered by your nightmare, however, you decide to consider actually doing some studying. You believe that with some studying you can improve your chances of choosing the
The Fred Meyer store in Portland has just received a large shipment of fitted baseball caps from Gradient Sporting Goods. In previous orders, a number of the hat sizes have been mislabeled. Because of this, the shipping and receiving manager plans to randomly check 20 of the hats in the current
Refer to the situation described in Exercise 77. Suppose the store has recently adopted a standard policy on shipment quality: If the overall shipment contains no more than 5% mislabeled hats, it should be considered “good” (that is, it is of acceptable quality). More than 5% mislabeled hats
Aerospace engineer turned baseball writer Eric Walker writes that the most important statistic for a baseball player is “on-base percentage” which basically measures “the probability that a batter will not make an out”. Suppose all the players for the Orchard Park Mangos have an on-base
For the probability distribution you produced in Exercise 1, a. Show the appropriate graph.b. Compute the expected value, the variance and the standard deviation of the random variable.
Use the Poisson function to determine the following probabilities: a. P(x = 2), where λ = 3b. P(x = 4), where λ = 1c. P(x = 3), where λ = 6
Use the Poisson table to confrm your answers in Exercise 80. a. P(x = 2), where λ = 3 b. P(x = 4), where λ = 1 c. P(x = 3), where λ = 6
Use the Poisson table toa. Sketch the Poisson distribution for λ = 2.b. Compute the mean and the standard deviation to verify that the mean is, in fact, λ and the standard deviation is equal to the square root of λ.
Traffic exiting the Arlington Turnpike at Exit 123 conforms roughly to the Poisson conditions. The average number of cars exiting is 6 per minute. Compute the probability ofa. Exactly 4 cars exiting during the next minute observed.b. At least 10 cars exiting during the next minute observed.c. No
The appearance of bubbles in the plastic sheets produced by Cumberland’s new extrusion equipment meets the Poisson conditions. The average number of bubbles per square yard of product is 0.2 (otherwise, the appearance of bubbles seems perfectly random and independent). Compute thea. Probability
Arrivals at the parking lot close to your job follow an approximately Poisson pattern, with a mean arrival rate of 10 cars per hour. You arrive at 9 A.M. and fnd that there are fve available spaces (of a total of 20 in the lot). You know that your boss will be arriving at 9:30, and will need a
Equipment malfunctions on the shop floor at Kai-Tak’s main manufacturing facility occur at an average rate of one per hour (otherwise, the malfunctions appear to be random and independent). Use the Poisson distribution to determine the probability ofa. Exactly two malfunctions in the next hour.b.
Refer to Exercise 86. Suppose Kai-Tak currently has a maintenance crew capable of effectively handling up to (and including) 10 malfunctions per 8-hour shiftIn Exercise 86Equipment malfunctions on the shop floor at Kai-Tak’s main manufacturing facility occur at an average rate of one per hour
Typographical errors in the Daily Times Mirror occur at an average rate of .4 per page. (The errors are random and independent.) Use the Poisson distribution to determine the probability of fnding no errorsa. On a randomly selected page.b. In the entire Sports section (11 pages).c. How likely is it
Use the Poisson table to approximate the following binomial probabilities: a. P(x = 7), where n = 100, p = .04 b. P(x = 4), where n = 80, p = .025 c. P(3 < x < 6), where n = 120, p = .01 d. P(x > 2), where n = 75, p = .02
For the probability distribution you produced in Exercise 2, a. Show the appropriate graph. b. Compute the expected value, the variance and the standard deviation of the random variable.
Use the binomial and the Poisson tables to compute and compare the binomial probabilities and the approximating Poisson probabilities for the following cases: a. P(x = 2), where n = 10, p = .05 b. P(x = 1), where n = 30, p = .10 c. P(1 < x < 3), where n = 20, p = .15 d. P( x = 2), where n = 5, p =
Andres, Beth and Charlie do cold call sales for their investment firm. Today they’ve made a little bet. The first one to talk to a “live” person when they make a call wins. They will call sequentially, with Andres going first, Beth going second, and Charlie going third, and will continue
The CEO and the CFO at Triton Capital will join the CEOs and CFOs of two other companies at a conference in Washington, DC. If the six corporate officers attending the conference are randomly seated at a round table in the main conference room,a. What is the probability that both Triton Capital
The useful life of electrical circuits produced by your company has a uniform distribution defend by the probability density function:where x = values for the random variable “useful circuit life in hours” a. Determine the probability that useful circuit life will be between 1060 and
Use the standard normal table in Appendix A to find the area a. Above (that is, to the right of) a point that’s 2.0 standard deviations below the mean. b. In an interval starting 1.57 standard deviations to the right of the mean and ending 2.36 standard deviations to the right of the mean. c.
Use the standard normal table in Appendix A. a. Find the point, z, above which we would find approximately 5% of the values in a standard normal distribution. b. Find the point, z, below which we would find approximately 10% of the values in a standard normal distribution.
The Oregon Fisheries Commission monitors the size of the salmon that climb the fish ladder at Bonneville Dam on the Columbia River every year. The Commission described the length of the salmon observed during the past year with a normal distribution having a mean of 78 cm and a standard deviation
The President’s Economic Advisory Council publishes an economic forecast every year. In the latest report, a normal distribution is used to describe the possible percentage change in US GDP (Gross Domestic Product) for the upcoming year. The distribution is centered on a rate of 4.2% and has a
As part of its effort to schedule television coverage for its major events, the ATP (Association of Tennis Professionals) keeps track of match times in tournaments. The organization has found that the distribution of match times is approximately normal, with a mean of 128 minutes and a standard
Cell phone usage in Vietnam has grown dramatically in the last few years, drawing the interest of a number of international telecommunications companies. A study done by the country’s Communications Ministry reports that the average time that cell phone subscribers spent on their cell phone
Harada Construction has just bid on a major commercial project. The bid was based on a normal distribution representing Harada’s estimates of possible costs for the project. The distribution is centered on $6.5 million and has a standard deviation of $1.1 million.a. How likely is it that project
According to a recent Gallup Poll, American men, on average, say they weigh 196 lbs.; women say they weigh 160 lbs. (source: Gallup.com). The sign in the main elevator in the new River Park Municipal Building identifies the maximum capacity of the elevator as 10 people, based on an average
In her 2011 book, author and video game designer Jane McGonigal reports, “The average young person racks up 10,000 hours of video gaming by the age of 21. That’s almost exactly as much time as they spend in a classroom during all of middle school and high school if they have perfect
In Exercise 16, we saw the following situation: Harada Construction has just bid on a major commercial project. The bid was based on a normal distribution representing Harada’s estimates of possible costs for the project. The distribution is centered on $6.5 million and has a standard deviation
Weight loss after two months on the Davies Diet has a uniform distribution defined by the following probability density function:where x = values for the €œweight loss€ random variable. a. Determine the probability that weight loss will be between 18 and 21 lbs. b. Determine the
Metropolitan Power and Light (MPL) tracks peak power usage, measured in gigawatts (GW), for its service area. MPL reports that in January peak daily demand for electrical power follows a normal distribution, with a mean of 4.3 GW and a standard deviation of .8 GW. For a randomly selected January
The Interior Department reports annually on the status of the country’s national forests. In a recent survey done in John Muir Woods in California, the Department used a normal curve to describe the age distribution of trees in the forest. The distribution has a mean of 143 years and a standard
An initial public offering (IPO) is the first sale of stock by a private company to the public. In a study of more than 4000 IPOs, researchers found the average annual return over a five-year period for firms issuing an IPO was 5.1. If the distribution describing the returns reported for all the
IQ tests have been used for more than a century to try to measure human intelligence. (They were originally intended to identify children who needed special education.) When an IQ test is developed, a sample representing the general population is given the test. The median score in the sample is
One of the weaving machines used by workers at Fleece-in-Our-Time to produce wool jackets and vests slips out of adjustment an average of 2.5 times per 10-hour shift (λ = .25 adjustment problems per hour). Assume all the Poisson conditions regarding independence, etc., are met. How likely is it
A recent study reports that the average number of severe potholes per mile of Interstate 576 is 4.0 (λ = 6 potholes per mile). The occurrences appear random and unrelated. Assume all the Poisson conditions regarding independence, etc., are met. You have just learned that one of your company’s
Tomoko Arakawa, a clerk at the Department of Motor Vehicles, processes customers at an average rate of 6 per hour (λ = 6 customers per hour). Assume all the Poisson conditions regarding independence, etc., are met. How likely is it that a randomly selected customer will take? a. At least 15
According to the US Geological Survey, on average there are 150 earthquakes of magnitude 6.0 or greater per year worldwide, which translates to an average of .41 quakes per day (source: earthquake.usgs.gov). Assume that all the Poisson conditions regarding independence, etc., are met. How likely is
The number of minutes of hot water you can expect from the shower in your dormitory is defined by the probability density function:where x = values for the random variable “minutes of hot water” a. Determine the probability that you will have between 5 and 5.5
During the month of September, the most active month for hurricanes on the Atlantic side of the United States, an average of 2.4 hurricanes strike the US coastline (source: aoml.noaa.gov). Assume this average holds and that all the Poisson conditions are met. a. What is the expected time, in
The average time between major claims at Secure Future Insurance is 2.2 weeks. If the time between claims has an exponential distribution, a. What is the average number of claims per day? b. What is the standard deviation (in days) of the exponential distribution here? c. How likely is it that the
Hybrid car batteries have an estimated average life of eight years. Using this average, if battery life has an exponential distribution, how likely is it that a random hybrid battery will have a life of a. At least 6 years? b. Between 7 and 9 years? c. Less than 5 years?
An average of four trucks per hour arrive at the receiving dock at Yuri Industries. No trucks have arrived in the last half-hour. Assuming that all Poisson conditions are met, determine the probability that you will need to wait a. At least 45 more minutes before the next truck arrives. b. Less
The time it takes for a customer to transact business at the window of the US Post Office branch in Sweet Briar, Texas, is exponentially distributed with a mean of 5.0 minutes. Four customers have just been processed in the last two minutes. How likely is it that the next customer will take a. More
According to auto insurance statistics, the average useful life for a car in the United States is 10 years. Assume the distribution of useful life is uniform, with the following probability density functionwhere x = values for the random variable “useful car life in years” a. What
A survey done for the Bermuda tourist industry reported that the average cruise ship visitor to Bermuda spends $185 for souvenirs, etc. (source: BermudaSun.org). Assume the distribution of visitor spending is uniform, and described by the probability density functionwhere x = values for the
Use the standard normal table to determine that probability that a. z is between 0 and 1.2; that is, find P(0 ≤ z ≤ 1.2). b. z is greater than or equal to 1.85; that is, find P(z ≥ 1.85). c. z is between 1 and 2; that is, find P(1 ≤ z ≤ 2). d. z is between – 1.93 and + 1.22;
Use the standard normal table to determine that probability that a. z is between 0 and 1; that is, find P(0 ≤ z ≤ 1). b. z is greater than or equal to 1.5; that is, find P(z ≥ 1.5). c. z is between 2 and 3; that is, find P(2 ≤ z ≤ 3). d. z is between – 1.35 and + 1.82; that
Use the standard normal table to determine that probability that a. z is between 0 and 1.48; that is, find P(0 ≤ z ≤ 1.48). b. z is greater than or equal to 2.67; that is, find P( z ≥ 2.67). c. z is between 2.2 and 2.55; that is, find P(2.2 ≤ z ≤ .55). d. z is between – 1.1 and +
The mature height of blue aster plants treated with Sun’s Natural Energy plant food can vary between 10 and 18 inches, and has a uniform probability distribution over this range of values. Define the probability density function here and use it to do what’s required below: a. Determine the
What percentage of values in a normal distribution will be a. Between the mean and a point 1.36 standard deviations to the right of the mean? b. In an interval that starts at 1.25 standard deviations to the left of the mean and extends to 1.65 standard deviations to the right of the mean? c.
What percentage of values in a normal distribution will be a. Between the mean and a point 1.75 standard deviations to the left of the mean? b. Below 2.33 standard deviations to the left of the mean? c. In an interval that starts at 1.0 standard deviations to the left of the mean and extends to
The amount of biodegradable waste material produced each day by your manufacturing operations has a normal distribution, with a mean of 250 tons and a standard deviation of 10 tons. Using x to represent the random variable “tons of waste,” find a. P(240 ≤ x ≤ 260) b. P(250 ≤ x ≤ 275) c.
Your form produces precision engine parts that must conform to fairly rigid diameter specifications. Diameters follow a normal distribution with a mean of 125 mm and a standard deviation of 4 mm. What percentage of diameters will be? a. Between 120 and 130 mm? b. Between 131 and 133 mm? c. Less
The average number of shares traded daily on the New York Stock Exchange during the past year was 1.9 million. If the distribution of daily trading volume is approximately normal, with a center at 1.9 million shares and a standard deviation of .25 million shares, on what percentage of the days was
The following table summarizes the average annual return and the standard deviation of returns for several types of securities over the past 75 years.Assume annual returns in each case are approximately normally distributed around the mean rate. Using this historical information as the basis for
Refer to Exercise 45. a. Suppose you invest $10,000 in large-cap stocks. Using the historical performance data shown in the table, how likely is it that you will end up making more than $4400 for the year? b. Suppose you invest $10,000 in long-term bonds. How likely is it that you will end up
The time of deployment (that is, the continuous time spent away from home port) for British sailors has a normal distribution, with a mean of 194 days and a standard deviation of 42 days. What percentage of the deployments were a. Less than 150 days? b. Between 200 and 220 days? c. Longer than 6
Use the standard normal table to determine the z-score necessary to construct a symmetric interval around the mean of a normal distribution in order to bound a. 90% of the values in the distribution. b. 95% of the values in the distribution. c. 99% of the values in the distribution.
Annual salaries at Courtney-Davies Worldwide Consulting follow an approximately normal pattern, with a mean wage of $82,300 and a standard deviation of $12,400. If an employee is randomly selected, how likely is it that the employee’s salary is a. Between $88,000 and $104,000? b. Between $75,000
The angle at which any one of Robbins Industries metal shaving machine camshafts comes to rest after spinning has a uniform distribution defined by the density functiona. Determine the probability that the resting position angle will be between 60 and 90 degrees. b. Determine the probability
In a study of cell phone service released by J.D. Power and Associates in 2012 (source: jdpower.com), the aver-age time that customers who called their cell phone company were put on hold before they were able to speak to a customer service representative was 4.6 minutes. Assume the distribution of
The germination time for a newly developed seed has a normal distribution, with a mean germination time of 16.4 days and a standard deviation of 2.2 days. a. What percentage of the seeds has a germination period between 15 and 18 days? b. What percentage of the seeds has a germination period less
Monthly demand for Cobalt’s new running shoe follows a normal distribution with a mean of 11,000 units and a standard deviation of 1000 units. Suppose Cobalt plans to produce 12,000 units for the upcoming month. a. How likely is it that the company will end up with at least 1500 units of unsold
Refer to Exercise 43 and answer the following questions: a. Quality control inspectors reject any part with a diameter less than 118 mm or more than 132 mm. What percentage of the parts is rejected? b. Suppose your engineers could reduce the variation in diameters. Specifically, suppose they can
Basset’s Liquid Filler III is a machine that falls containers with a preset amount of semi-liquid product that will be used in its plastics molding process. The average fill weight for the machine can be set and controlled, but there is inevitably some variability in the process. Actual
Armstead Tires produces tires with a useful life that follows a normal pattern. Average life is 36,000 miles, with a standard deviation of 1500 miles. a. What percentage of the tires will have a useful life between 38,000 and 40,000 miles? b. What percentage of the tires will have a useful life
Over the years, attendance at the International Tele communications Conference in Brussels, hosted annually by the five largest firms in the telecommunications industry, has followed an approximately normal pattern, with a mean of 1560 attendees and a standard deviation of 240. a. Using this
The national average cost per student for books and supplies at four-year private colleges in 2011–2012 was $1,213. Assume the same average is true for the upcoming school year and these expenses are approximately normally distributed, with a standard deviation of $68. a. What percentage of
The Los Angeles County Fire Department’s Air Operations wing, headquartered in Pacoima, answers an average of 1800 emergency medical calls a year, or approximately five calls per day (source : Los Angeles Times). Assume that emergency calls meet all the Poisson conditions. a. How likely is it
The waiting time for customers who place an order at Quick-n-Tasty Chicken is exponentially distributed, with an average waiting time of 2.5 minutes. How likely is it that a customer will wait? a. At least 3 minutes? b. Less than 2 minutes? c. Between 4 and 5 minutes?
The distance from a random leak in an oil pipeline made up of 30-foot segments to the segment end nearest the leak (where the pipeline would be opened in order to get inside to make repairs) has a uniform distribution defined by the density functiona. Determine the probability that the
Records kept at Boston’s Brigham Hospital show an average of 1.4 maternity patients per hour check in during the 8 P.M. to 2 A.M. shift (that is, λ = 1.4 check-ins per hour). Assume that maternity patient check-ins meet all the Poisson conditions. a. How likely is it that less than a half-hour
During the hours of 3 P.M. to 10 P.M., the average (or expected) time it takes to serve the steady stream of ticket buyers at the ticket window of the Rialto Multiplex Theater is 45 seconds per customer. All the conditions for a Poisson distribution are met. a. Use the exponential distribution
You have the option of catching a train to work every day at either the L Street Station or the M Street Station. At either station, trains arrive on average every two minutes. That is, each station is served by an average of 30 trains per hour. The train line serving the L Street Station stops at
Use the standard normal table in Appendix A to find the area a. At or below a point 1.64 standard deviations to the right of the mean. b. At or below a point 2.33 standard deviations to the left of the mean. c. In an interval starting 2.15 standard deviations to the left of the mean and ending
Use the standard normal table in Appendix A to find the area a. Out beyond 1.96 standard deviations to the right of the mean. b. In an interval starting .6 standard deviations to the right of the mean and ending 1.6 standard deviations to the right of the mean. c. In an interval starting 1.2
Use the standard normal table in Appendix A to find the area a. Above (that is, to the right of) a point that’s 1.96 standard deviations below the mean. b. in an interval starting 1.36 standard deviations to the right of the mean and ending 2.22 standard deviations to the right of the
Certification Magazine conducted a salary survey of US IT (Information Technology) professionals, contacting a simple random sample of 7130 certified IT specialists. The sample average salary was $96,677. a. Estimate the average salary for the population of IT professionals
Refer to Exercise 59. Suppose the sample size had been only 12 instead of 100. Suppose, too, that the population standard deviation is unknown, but the sample standard deviation is 83 points. a. Show the 95% confidence interval that would be appropriate here. b. What additional assumption
Refer to Exercise 61. Suppose the sample size here had been 20 instead of 49. Suppose, too, that the population standard deviation is unknown, but the sample has a standard deviation of 5.2 years. a. Show the 95%, the 99% and the 80% intervals that would be appropriate here. b. What additional
The QC department at Hershey Mechanical wants to estimate the average useful life of the new O-ring seals that the company has just put on the market. A simple random sample of 25 O-rings produces a sample average life of 1560 hours. The sample standard deviation is 68 hours. a. Construct and
Sora-Tobu-Jutan Technologies wants to estimate the aver-age time it takes to complete the assembly of its new robot vacuum cleaner. After allowing enough time for the workers to learn the new assembly procedures, supervisors choose 15 assemblies to observe. For these 15 assemblies, average assembly
Fence-U-In is testing the breaking strength of the chain links the company produces for its fencing products. Suppose a sample of five links is selected, with the following test results:Produce the 90% confidence interval. Assume that the population of breaking strength values is approximately
As part of a marketing study, Sleep ’n’ Dream wants to estimate, for customers who have recently purchased a mattress and box spring, the average number of stores that customers visited before making their purchase. A sample of six customers is randomly selected, with the following results:Use
Koufos Imports wants to estimate the average value of its current accounts receivable. In all, there are 2000 accounts. A simple random sample of 40 accounts is selected. The average amount due the firm in the sample is $6500. The sample standard deviation is $1600. a. Show the 95% confidence
Brill’s Deli owns a feet of four delivery trucks. The odometer readings for the four trucks are shown below:a. Show the six equally likely samples of size two that could be selected from this truck population. b. Show the mean odometer reading for each of the six
Researchers plan to estimate the average daily output for the 2300 firms in the metal fabricating industry. You randomly select 60 of the firms and find that the average daily output for firms in the sample is 1560 units, with a sample standard deviation of 320 units. a. Construct a 99% confidence
The annual forecast of Florida’s grapefruit crop is based on an actual count of the grapefruits on a random sample of trees. Suppose five grapefruit trees are selected at random and the fruit on each tree is counted. Results of the count are given below:a. Build a 95% confidence interval estimate
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