Questions and Answers of Applied Statistics and Probability

Zeitler€™s Department Stores sells its products online and through traditional brick-andmortar stores. The following parallel-coordinates plot displays data from a sample of 20 customers
During each month, there is enough production capacity to produce up to 32,000 total balls (football 1 soccer balls), and there is enough storage capacity to store up to 20,000 total balls (football
A European put option on a currency allows you to sell a unit of that currency at the specified strike price (exchange rate) at a particular point in time after the purchase of the option. For
As admissions director for an exclusive executive MBA program which takes place on Necker Island in the Caribbean, Richard Branson must decide which applicants should receive admission offers. This
Bianca Peterson is a marketing engineer for Hexagon Composites, a company which sells carbon composite storage tanks. In an effort to gain product adoptions from customers, Bianca goes on sales trips
Young entrepreneur Fan Bingbing has launched a business venture in which she uses stories submitted by university students as the basis for comics in a monthly animestyle magazine. Based on market
Steve Austin is the fleet manager for SharePlane, a company that sells fractional ownership of private jets. SharePlane must carefully maintain their jets at all times. If a jet breaks down, it must
You are considering the purchase of a new car and are weighing the choice between a Ford Fusion Hybrid sedan (which assists a gasoline engine with an electric motor powered via regenerative braking)
Using the file LandSharkBeta, evaluate bid amounts from $1,229,000 to $1,329,000 in increments of $20,000 by building a table listing 95% confidence intervals around the average return and
The Dallas Mavericks and the Golden State Warriors are two teams in the National Basketball Association. Dallas and Golden State will play multiple times over the course of an NBA season. Assume that
Goal Kick Sports (GKS) is a retail chain that sells youth and adult soccer equipment. The GKS financial planning group has developed a spreadsheet model to calculate the net discounted cash flow of
A well-respected polling agency has conducted a poll for an upcoming Presidential election. The polling agency has taken measures so that its random sample consists of 50,000 people and is
A random variable has a triangular probability density function with a = 50, b = 375, and m = 250.a. Sketch the probability distribution function for this random variable. Label the points a = 50, b
The online review service Yelp helps millions of consumers find the goods and services they seek. To help consumers make more-informed choices, Yelp includes over 120 million reviews. The file
Companies can learn a lot about customer experiences by monitoring the social media web site Twitter. The file AirlineTweets contains a sample of 36 tweets of an airline’s customers. Normalize the
Josephine Mater works for the supply-chain analytics division of Trader Joe’s, a national chain of specialty grocery stores. Trader Joe’s is considering a redesign of its supply chain. Josephine
Apply k-means clustering with values of k = 2, 3, 4, and 5 to cluster the data in DemoKTC based on the Age, Income, and Children variables. Normalize the values of the input variables to adjust for
Leggere, an internet book retailer, is interested in better understanding the purchase decisions of its customers. For a set of 2,000 customer transactions, it has categorized the individual book
Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table.Jay has
Amanda Boleyn, an entrepreneur who recently sold her start-up for a multi-million-dollar sum, is looking for alternate investments for her newfound fortune. She is considering an investment in wine,
In an effort to inform political leaders and economists discussing the deregulation of electric and gas utilities, data on eight numerical variables from utility companies have been grouped using
The regulation of electric and gas utilities is an important public policy question affecting consumer€™s choice and cost of energy provider. To inform deliberation on public policy, data
For this problem we will use the data in the file Global100 that was referenced in Section 3.4 as an example for creating a treemap. Here we will use these data to create a GIS chart. A portion of
Approximately 1.65 million high school students take the Scholastic Aptitude Test (SAT) each year, and nearly 80% of the college and universities without open admissions policies use SAT scores in
Huron Lakes Candies (HLC) has developed a new candy bar called Java Cup that is a milk chocolate cup with a coffee-cream center. In order to assess the market potential of Java Cup, HLC has developed
Marilyn Marshall, a Professor of sports economics, has obtained a data set of home attendance for each of the 30 major league baseball franchises for each season from 2010 through 2016. Dr. Marshall
The following table shows an example of gross domestic product values for five countries over six years in equivalent U.S. dollars ($).a. How could you improve the readability of this table?b. The
Below is a sample of the data in the file NFLAttendance which contains the 32 teams in the National Football League, their conference affiliation, their division, and their average home attendance.a.
Analyze the develop or contract decision problem in Example 15-9 based on the best-case (optimistic) criterion and determine the actions selected at each decision node. Do any actions differ from
Reconsider the extended warranty decision in Example 15-8. Determine the cost of the extended warranty so that the expected costs of the actions to either purchase the warranty or not are
Suppose that a P chart with center line at p̅ and k-sigma control limits is used to control a process. What is the smallest sample size that can be used on this control chart to ensure that the
Suppose that a P chart with center line at p with k-sigma control limits is used to control a process. There is a critical fraction defective pc that must be detected with probability 0.50 on the
Suppose that an X̅ chart is used to control a normally distributed process and that samples of size n are taken every n hours and plotted on the chart, which has k-sigma limits.(a) Find a general
Consider an X̅ control chart with k-sigma control limits and subgroup size n. Develop a general expression for the probability that a point plots outside the control limits when the process mean has
Suppose that a process is in control, and 3-sigma control limits are in use on an X̅ chart. The subgroup size is 4. Let the mean shift by 1.5σ. What is the probability that this shift remains
Consider the infectious-waste data in Exercise 15-26. Use the data after the process change only.(a) Construct an CUSUM control chart with the target equal to the estimated process mean, k = 0.5, and
An article in Electric Power Systems Research [€œOn the Self-Scheduling of a Power Producer in Uncertain Trading Environments€ (2008) considered a self-scheduling approach for a
Consider the TAT data in Exercise 15-18.(a) Construct an CUSUM control chart with the target equal to the estimated process mean, k = 0.5, and h = 4. Does the process appear to be in control at the
A process is controlled by a P chart using samples of size 100. The center line on the chart is 0.05.(a) What is the probability that the control chart detects a shift to 0.08 on the first sample
Analyze Example 15-9 based on the expected profit criterion and determine the actions that are selected at each decision node. Do any actions differ from those selected in the example?Example 15-9In
Analyze Example 15-9 based on the most probable criterion and determine the actions that are selected at each decision node. Do any actions differ from those selected in the example?Example 15-9In
Reconsider the extended warranty decision in Example 15-8. Suppose that the probabilities of the major, minor, and no repair states are changed to 0.2, 0.4, and 0.4, respectively. Determine the
Suppose that the cost of a major repair without the extended warranty in Example 15-8 is changed to $1000. Determine the decision selected based on the minimax, most probable, and expected cost
Consider an EMWA control chart. The target value for the process is Î¼0= 50 and Ïƒ = 2. Use Table 15-11.(a) If the sample size is n = 1, would you prefer an EWMA chart with
Consider the concentration data in Exercise 15-76. Use σ = 8 and assume that the desired process target is 100.(a) Construct an EWMA control chart with λ = 0.2. Does the process appear to be in
Consider the diameter data in Exercise 15-75. Assume that the desired process target is 10.0 millimeters.(a) Estimate the process standard deviation.(b) Construct an EWMA control chart with
Consider the purity data in Exercise 15-74. Use Ïƒ = 0.8 and assume that the desired process target is 90. (a) Construct an EWMA control chart with Î» = 0.2. Does the
Consider a CUSUM with h = 5 and k = 1 / 2. Samples are taken every two hours from the process. The target value for the process is Î¼0= 50 and Ïƒ = 2. Use Table 15-10.Table
The concentration of a chemical product is measured by taking four samples from each batch of material. The average concentration of these measurements for the last 20 batches is shown in the
An automatic senson measures the diameter of holes in consecutive order. The results of measuring 25 holes follow.(a) Estimate the process standard deviation.(b) Set up a CUSUM control procedure,
The purity of a chemical product is measured every two hours. The results of 20 consecutive measurements are as follows:(a) Set up a CUSUM control chart for this process. Use Ïƒ = 0.8 in
The following data were considered in Quality Engineering [€œParabolic Control Limits for The Exponentially Weighted Moving Average Control Charts in Quality Engineering€ (1992,
Consider the U chart for printed circuit boards in Example 15-5. The center line = 1.6, UCL = 3.3, and n = 5.(a) Calculate the LCL and UCL.(b) Suppose that the true mean defects per unit shifts from
Consider a P-chart with subgroup size n = 50 and center line at 0.12.(a) Calculate the LCL and UCL.(b) Suppose that the true proportion defective changes from 0.12 to 0.18. What is the ARL after the
Consider an X̅ control chart with UCL = 24.802, LCL = 23.792, and n = 3. Suppose that the mean shifts to 24.2.(a) What is the probability that this shift is detected on the next sample?(b) What is
An X̅ chart uses a sample of size 3. The center line is at 200, and the upper and lower 3-sigma control limits are at 212 and 188, respectively.(a) Estimate the process σ.(b) Suppose that the
Consider the revised XÌ… control chart in Exercise 15-8 with ÏƒÌ‚ = 0.669, UCL = 7.443, LCL = 5.125, and n = 3. Suppose that the mean shifts to 5.5.(a) What is the
Consider an X̅ control chart with r̅ = 0.000924, UCL = 0.0635, LCL = 0.0624, and n = 5. Suppose that the mean shifts to 0.0625.(a) What is the probability that this shift is detected on the next
Consider an X̅ control chart with r̅ = 2.25, UCL = 17.40, LCL = 12.79, and n = 3. Suppose that the mean shifts to 13.(a) What is the probability that this shift is detected on the next sample?(b)
Consider an X̅ control chart with σ̂ = 2.466, UCL = 37.404, LCL = 30.780, and n = 5. Suppose that the mean shifts to 36.(a) What is the probability that this shift is detected on the next
Consider an X̅ control chart with σ̂ = 1.40, UCL = 21.71, LCL = 18.29, and n = 6. Suppose that the mean shifts to 17.(a) What is the probability that this shift is detected on the next sample?(b)
Consider an X̅ control chart with r̅ = 34.286, UCL = 242.780, LCL = 203.220, and n = 5. Suppose that the mean shifts to 210.(a) What is the probability that this shift is detected on the next
Consider an X̅ control chart with r̅ = 0.344, UCL = 14.708, LCL = 14.312, and n = 5. Suppose that the mean shifts to 14.6.(a) What is the probability that this shift is detected on the next
Consider the X control chart in Fig. 15-3. Suppose that the mean shifts to 74.010 millimeters.(a) What is the probability that this shift is detected on the next sample?(b) What is the ARL after the
An X̅ chart uses samples of size 4. The center line is at 100, and the upper and lower 3-sigma control limits are at 106 and 94, respectively.(a) What is the process σ?(b) Suppose that the process
An X chart uses samples of size 1. The center line is at 100, and the upper and lower 3-sigma limits are at 112 and 88, respectively.(a) What is the process σ?(b) Suppose that the process mean
A article in Graefe€™s Archive for Clinical and Experimental Ophthalmology [€œStatistical Process Control Charts for Ophthalmology,€ considered the number of cataract
A article of Epilepsy Research [€œStatistical Process Control (SPC): A Simple Objective Method for Monitoring Seizure Frequency and Evaluating Effectiveness of Drug Interventions in
The following data are the number of spelling errors detected for every 1000 words on a news Web site over 20 weeks.(a) What control chart is most appropriate for these data?(b) Using all the data,
In a semiconductor manufacturing company, samples of 200 wafers are tested for defectives in the lot. See the number of defectives in 20 such samples in the following table.(a) Set up a P chart for
Consider the data on the number of earthquakes of magnitude 7.0 or greater by year in Exercise 6-87.(a) Construct a U chart for this data with a sample size of n = 1.(b) Do the data appear to be
The following represent the number of solder defects observed on 24 samples of five printed circuit boards: 7, 6, 8, 10, 24, 6, 5, 4, 8, 11, 15, 8, 4, 16, 11, 12, 8, 6, 5, 9, 7, 14, 8, 21.(a)
The following represent the number of defects per 1000 feet in rubber-covered wire: 1, 1, 3, 7, 8, 10, 5, 13, 0, 19, 24, 6, 9, 11, 15, 8, 3, 6, 7, 4, 9, 20, 11, 7, 18, 10, 6, 4, 0, 9, 7, 3,1, 8,
The following are the numbers of defective solder joints found during successive samples of 500 solder joints:(a) Using all the data, compute trial control limits for a fraction- defective control
Suppose that the following fraction defective has been found in successive samples of size 100 (read down):(a) Using all the data, compute trial control limits for a fraction- defective control
Consider the inventory accuracy in Exercise 15-27. Because lower values are better, only the UCL = 0 3 . is specified. Use the revised control chart to calculate PCRk.Exercise 15-27An article in
Consider the turnaround time (TAT) for complete blood counts in Exercise 15-18. Suppose that the specifications for TAT are set at 20 and 80 minutes. Use the control chart summary statistics for the
The control limits for an X̅ chart with n = 4 are 12.8 and 24.8, and the PCR for a measurement is 1.33.(a) Estimate the process standard deviation σ.(b) Calculate the specification limits. Assume
A article in the Journal of Quality in Clinical Practice [€œThe Application of Statistical Process Control Charts to the Detection and Monitoring of Hospital-Acquired
An article in Microelectronics Reliability [€œAdvanced Electronic Prognostics through System Telemetry and Pattern Recognition Methods,€ (2007, 47(12), pp. 1865€“1873)] presented an
The number of visits (in millions) on a Web site is recorded every day. The following table shows the samples for 25 consecutive days.(a) Estimate the process standard estimation.(b) Set up a CUSUM
Consider an X̅ control chart with UCL = 32.802, UCL = 24.642, and n = 5. Suppose that the mean shifts to 30.(a) What is the probability that this shift is detected on the next sample?(b) What is the
The following are the number of defects observed on 15 samples of transmission units in an automotive manufacturing company. Each lot contains five transmission units.(a) Using all the data, compute
The following table shows the number of e-mails a student received each hour from 8:00 a.m. to 6:00 p.m. The samples are collected for five days from Monday to Friday.(a) Use the rational subgrouping
The following table provides the costs for gasoline by month in the United States over recent years and the percentage of the cost due to refining, distribution and marketing, taxes, and crude oil.
An EWMA chart with λ = 0.5 and L = 3.07 is to be used to monitor a process. Suppose that the process mean is μ0 = 10 and σ = 2.(a) Assume that n = 1. What is the ARL without any shift in the
Suppose that the average number of defects in a unit is known to be 10. If the mean number of defects in a unit shifts to 14, what is the probability that it is detected by a U chart on the first
Suppose that the average number of defects in a unit is known to be 8. If the mean number of defects in a unit shifts to 16, what is the probability that it is detected by a U chart on the first
Suppose that a process has a PCR = 2, but the mean is exactly 3 standard deviations above the upper specification limit. What is the probability of making a product outside the specification limits?
Consider a control chart for individuals with 3-sigma limits. What is the probability that there is not a signal in 3 samples? In 6 samples? In 10 samples?
The depth of a keyway is an important part quality characteristic. Samples of size n = 5 are taken every four hours from the process, and 20 samples are summarized in the following table.(a) Using
Consider a control chart for individuals applied to a continuous 24-hour chemical process with observations taken every hour.(a) If the chart has 3-sigma limits, verify that the in-control ARL is
Consider the control chart for individuals with 3-sigma limits.(a) Suppose that a shift in the process mean of magnitude σ occurs. Verify that the ARL for detecting the shift is ARL = 43.9.(b) Find
Suppose that a process is in control and an X chart is used with a sample size of 4 to monitor the process. Suddenly there is a mean shift of 1.5σ.(a) If 3-sigma control limits are used on the X
The following data were considered in Quality Progress [€œDigidot Plots for Process Surveillance€ (1990, May, pp. 66€“68)]. Measurements of center thickness (in mils)
Reconsider the viscosity data in Exercise 15-22. Construct a CUSUM control chart for this process using Î¼0= 500 as the process target. Explain how you determined your estimate of
Consider the hardness measurement data in Exercise 15-19. Set up a CUSUM scheme for this process using Î¼ = 50 and Ïƒ = 2 so that K = 1 and H = 10. Is the process in control?Exercise 15-19Twenty
Consider the data in Exercise 15-20. Set up a CUSUM scheme for this process assuming that Î¼ = 16 is the process target. Explain how you determined your estimate of Ïƒ and the
Consider the hub data in Exercise 15-95.(a) Construct an EWMA control chart with Î» = 0.2 and L = 3. Comment on process control.(b) Construct an EWMA control chart with Î» =
Consider the renewable energy data in Exercise 15-96.(a) Construct an EWMA control chart with Î» = 0.2 and L = 3. Do the data appear to be generated from an in control process?(b)

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