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statistics

Questions and Answers of Statistics

The following examples are experiments and their associated random variables. In each case identify the values the random variable can assume and state whether the random variable is discrete or
The following table shows a partial probability distribution for the MRA Company’s projected profits (in thousands of dollars) for the first year of operation (the negative value denotes a loss):x
Data were collected on the number of operating rooms in use at Tampa General Hospital over a 20-day period. On 3 of the days only one operating room was used; on 5 days, two were used; on 8 days,
Shown is a probability distribution for the random variable x.x f(x)3 .......0.256 ........0.509 .......0.25Total 1.00a. Compute E(x), the expected value of x.b. Compute σ2, the variance of x.c.
Shown are the percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers. The scores range from a low of 1 (very
The American Housing Survey reported the following data on the number of bedrooms in owner-occupied and renter-occupied houses in central cities (www.census.gov, March 31, 2003):a. Define a random
The demand for a product of Carolina Industries varies greatly from month to month. Based on the past two years of data, the following probability distribution shows the company’s monthly
The J. R. Ryland Computer Company is considering a plant expansion that will enable the company to begin production of a new computer product. The companyâ€™s president must determine whether to
Consider a binomial experiment with 2 trials and p =- 0.4.a. Compute the probability of 1 success, f(1).b. Compute f(0).c. Compute f(2).d. Find the probability of at least 1 success.e. Find the
Consider a binomial experiment with n = 10 and p = 0.10. Use the binomial tables (Appendix B) to answer parts (a) through (d).a. Find f (0).b. Find f (2).c. Find P(x ≤ 2).d. Find P(x ≥ 1).e. Find
AHarris Interactive survey for InterContinental Hotels & Resorts asked respondents, “When traveling internationally, do you generally venture out on your own to experience culture or stick with
When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number
Military radar and missile detection systems are designed to warn a country of enemy attacks. A reliability question deals with the ability of the detection system to identify an attack and issue the
Consider a Poisson probability distribution with 2 as the average number of occurrences per time period.a. Write the appropriate Poisson probability function.b. What is the average number of
Telephone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. a. Find the probability of receiving 3 calls in a 5-minute interval.b. Find the probability of
More than 50 million guests stayed at bed and breakfasts (B&Bs) last year. The Web site for the Bed and Breakfast Inns of North America (www.bestinns.com), which averages approximately seven
Airline passengers arrive randomly and independently at the passenger screening facility at a major international airport. The mean arrival rate is 10 passengers per minute.a. What is the probability
A random variable x is uniformly distributed between 1.0 and 1.5.a. Show the graph of the probability density function.b. Find P(x = 1.25).c. Find P(1.0 ≤ x ≤ 1.25).d. Find P(1.20 < x < 1.5).
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours,
Most computer languages have a function that can be used to generate random numbers. In Microsoft’s Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x
For the standard normal random variable z, compute the following probabilities:a. P(0 ≤ z ≤ 0.83)b. P(–1.57 ≤ z ≤ 0)c. P(z > 0.44)d. P(z ≥ 20.23)e. P(z < 1.20)f. P(z ≤ 20.71)
For the standard normal random variable z, find z for each situation.a. The area to the left of z is 0.9750.b. The area between 0 and z is 0.4750.c. The area to the left of z is 0.7291.d. The area to
For the standard normal random variable z, find z for each situation.a. The area to the left of z is 0.2119.b. The area between - z and z is 0.9030.c. The area between - z and z is 0.2052.d. The area
The demand for a new product is estimated to be normally distributed with µ = 200 and µ = 40. Let x be the number of units demanded and find the following probabilities:a. P(180 ≤ x ≤ 220)b.
The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $8.20 (BusinessWeek, Special Annual Issue, Spring 2003). Assume the stock prices are normally
General Hospital’s patient account division has compiled data on the age of accounts receivable. The data collected indicate that the age of the accounts follows a normal distribution with µ= 28
The Webster National Bank is reviewing its service charges and interest-paying policies on checking accounts. The average daily balance on personal checking accounts is $550, with a standard
A machine fills containers with a particular product. The standard deviation of filling weights computed from past data is 0.6 ounces. If only 2% of the containers hold less than 18 ounces, what is
Consider the exponential probability density function:f(x) = 1/3e–x/3 for x ≥ 0a. Write the formula for P(x ≤ x0).b. Find P(x ≤ 2).c. Find P(x ≥ 3).d. Find P(x ≤ 5).e. Find P(2 ≤ x ≤
Internet Magazine monitors Internet service providers (ISPs) and provides statistics on their performance. The average time to download a Web page for free ISPs is approximately 20 seconds for
The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds.a. Sketch this exponential probability distribution.b.
The lifetime (hours) of an electronic device is a random variable with the exponential probability density function:f(x) = 1/50e-x/50 for x ≥ 0a. What is the mean lifetime of the device?b. What is
The time (in minutes) between telephone calls at an insurance claims office has the exponential probability distribution:f(x) = 0.50e-.50x for x ≥ 0a. What is the mean time between telephone
Sparagowski & Associates conducted a study of service times at the drive-up window of fast-food restaurants. The average time between placing an order and receiving the order at McDonald’s
Corporate Triple A Bond interest rates for 12 consecutive months are 9.5, 9.3, 9.4, 9.6, 9.8, 9.7, 9.8, 10.5, 9.9, 9.7, 9.6, and 9.6.a. Develop three- and four-month moving averages for this time
Refer to the gasoline sales time series data in Table.a. Compute four- and five-week moving averages for the time series.b. Compute the MSE for the four- and five-week moving average forecasts.c.
Refer again to the gasoline sales time series data in Table.a. Use a weight of 1/2 for the most recent observation, 1/3 for the second most recent, and 1/6 for the third most recent to compute a
Use the gasoline sales time series data from Table to show the exponential smoothing forecasts using α = 0.1. Using the mean squared error criterion, would you prefer a smoothing constant of α =
For the Hawkins Company, the monthly percentages of all shipments that were received on time over the past 12 months are 80, 82, 84, 83, 83, 84, 85, 84, 82, 83, 84, and 83.a. Compare a three-month
With a smoothing constant of α = 0.2, equation (6.2) shows that the forecast for the 13th week of the gasoline sales data from Table is given by F13 = 0.2Y12 + 0.8F12. However, the forecast for week
Alabama building contracts for a 12-month period (in millions of dollars) are 240, 350, 230, 260, 280, 320, 220, 310, 240, 310, 240, and 230.a. Compare a 3-month moving average forecast with an
Moving averages often are used to identify movements in stock prices. Daily closing prices (in dollars per share) for SanDisk for August 16, 2002, through September 3, 2002, followa. Use a five-day
The following data represent 15 quarters of manufacturing capacity utilization (in percentages):a. Compute three- and four-quarter moving averages for this time series. Which moving average provides
For the 2001â€“2002 National Basketball Association season, Philadelphia 76ers Allen Iverson was the scoring leader with an average of 31.4 points per game. The following data show the average
The percentage of individual investorsâ€™ portfolios committed to stock depends on the state of the economy. The following table reports the percentage of stocks in a portfolio for nine
United Dairies, Inc., supplies milk to several independent grocers throughout Dade County, Florida. Management wants to develop a forecast of the number of half-gallons of milk sold per week. Sales
Ten weeks of data on the Commodity Futures Index are 7.35, 7.40, 7.55, 7.56, 7.60, 7.52, 7.52, 7.70, 7.62, and 7.55.a. Compute the exponential smoothing values for α = 0.2.b. Compute the exponential
The enrollment data (figures in thousands) for a state college for the past six years are shown.Develop the equation for the linear trend component for this time series. Comment on what is happening
The president of a small manufacturing firm has been concerned about the continual growth in manufacturing costs over the past several years. The following is a time series of the cost per unit (in
TV ratings provided by Nielsen Media Research show the percentage of TV-owning households tuned in to a particular program. The following data show the rating for the top-rated TV show of each
The Federal Election Commission maintains data showing the voting age population, the number of registered voters, and the turnout for federal elections. The following table shows the national voter
The following data show the time series of the most recent quarterly capital expenditures (in billions of dollars) for the 1000 largest manufacturing firms: 24, 25, 23, 24, 22, 26, 28, 31, 29, 32,
The Costello Music Company has been in business for five years. During that time, the sales of electric organs have grown from 12 units in the first year to 76 units in the most recent year. Fred
Hudson Marine has been an authorized dealer for C&D marine radios for the past seven years. The number of radios sold each year is shown.a. Graph this time series. Does a linear trend appear?b.
The League of American Theatres and Producers, Inc., collects a variety of statistics for Broadway plays, such as gross revenue, playing time, and number of new productions. The following data show
The Garden Avenue Seven sells tapes of its musical performances. The following data show sales for the past 18 months. The groupâ€™s manager wants an accurate method for forecasting future
The Mayfair Department Store in Davenport, Iowa, is trying to determine the amount of sales lost while it was shut down because of summer floods. Sales data for January through June are shown.Month
The quarterly sales data (number of copies sold) for a college textbook over the past three years are as follows:a. Show the four-quarter moving average values for this time series. Plot both the
Identify the monthly seasonal indexes for the following three years of expenses for a six-unit apartment house in southern Florida. Use a 12-month moving averagecalculation.
Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit
Refer to Problem 21. Suppose that the following are the quarterly sales data for the past seven years:a. Show the four-quarter moving average values for this time series. Plot both the original time
Consider the Costello Music Company scenario presented in Problem 20 and the following quarterly sales data:a. Compute the seasonal indexes for the four quarters.b. When does Costello Music
Refer to the Hudson Marine data in Problem 28.a. Deseasonalize the data, and use the deseasonalized time series to identify the trend.b. Use the results of part (a) to develop a quarterly forecast
Consider the Costello Music Company time series in Problem 29.a. Deseasonalize the data, and use the deseasonalized time series to identify the trend.b. Use the results of part (a) to develop a
Electric power consumption is measured in kilowatt-hours (kWh). The local utility company has an interrupt program, whereby commercial customers who participate receive favorable rates but must agree
Eddieâ€™s Restaurants collected the following data on the relationship between advertising and sales at a sample of five restaurants:a. Let x represent advertising expenditures and y represent
The management of a chain of fast-food restaurants wants to investigate the relationship between the daily sales volume (in dollars) of a company restaurant and the number of competitor restaurants
The supervisor of a manufacturing process believed that assembly-line speed (in feet/minute) affected the number of defective parts found during on-line inspection. To test this theory, management
The Vintage Restaurant is located on Captiva Island, a resort community near Fort Myers, Florida. The restaurant, which is owned and operated by Karen Payne, just completed its third year of
The Carlson Department Store suffered heavy damage when a hurricane struck on August 31, 2003. The store was closed for four months (September 2003 through December 2003), and Carlson is now involved
A company imports goods at two ports: Philadelphia and New Orleans. Shipments of one product are made to customers in Atlanta, Dallas, Columbus, and Boston. For the next planning period, the supplies
Consider the following network representation of a transportation problem:The supplies, demands, and transportation costs per unit are shown on the network.a. Develop a linear programming model for
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas.Demand forecasts for the
Arnoff Enterprises manufactures the central processing unit (CPU) for a line of personal computers. The CPUs are manufactured in Seattle, Columbus, and New York and shipped to warehouses in
Premier Consultingâ€™s two consultants, Avery and Baker, can be scheduled to work for clients up to a maximum of 160 hours each over the next four weeks. A third consultant, Campbell, has some
Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein€™s customers have already placed orders that together exceed the combined
Forbelt Corporation has a one-year contract to supply motors for all refrigerators produced by the Ice Age Corporation. Ice Age manufactures the refrigerators at four locations around the country:
The Ace Manufacturing Company has orders for three similar products:OrdersProduct (units)A ..........2000B .......... 500C ..........1200Three machines are available for the manufacturing operations.
Scott and Associates, Inc., is an accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders,
CarpetPlus sells and installs floor covering for commercial buildings. Brad Sweeney, a CarpetPlus account executive, was just awarded the contract for five jobs. Brad must now assign a CarpetPlus
Alocal television station plans to drop four Friday evening programs at the end of the season. Steve Botuchis, the station manager, developed a list of six potential replacement programs. Estimates
The U.S. Cable Company uses a distribution system with five distribution centers and eight customer zones. Each customer zone is assigned a sole source supplier; each customer zone receives all of
United Express Service (UES) uses large quantities of packaging materials at its four distribution hubs. After screening potential suppliers, UES identified six vendors that can provide packaging
The quantitative methods department head at a major midwestern university will be scheduling faculty to teach courses during the coming autumn term. Four core courses need to be covered. The four
A market research firm€™s three clients each requested that the firm conduct a sample survey. Four available statisticians can be assigned to these three projects; however, all four
Hatcher Enterprises uses a chemical called Rbase in production operations at five divisions. Only six suppliers of Rbase meet Hatcher€™s quality control standards. All six suppliers can
The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are
Refer to Problem 17. Suppose that shipments between the two warehouses are permitted at $2 per unit and that direct shipments can be made from plant 3 to customer 4 at a cost of $7 per unit.a.
Adirondack Paper Mills, Inc., operates paper plants in Augusta, Maine, and Tupper Lake, New York. Warehouse facilities are located in Albany, New York, and Portsmouth, New Hampshire. Distributors are
The Moore & Harman Company is in the business of buying and selling grain. An important aspect of the company€™s business is arranging for the purchased grain to be shipped to customers. If
The following linear programming formulation is for a transshipment problem:Show the network representation of thisproblem.
A rental car company has an imbalance of cars at seven of its locations. The following network shows the locations of concern (the nodes) and the cost to move a car between locations. A positive
Find the shortest route from node 1 to node 7 in the networkshown.
In the original Gorman Construction Company problem, we found the shortest distance from the office (node 1) to the construction site located at node 6. Because some of the roads are highways and
Cleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland met- ropolitan area. Most of CARDâ€™s business involves rapid delivery of documents and parcels between offices
Morgan Trucking Company operates a special pickup and delivery service between Chicago and six other cities located in a four-state area. When Morgan receives a request for service, it dispatches a
City Cab Company identified 10 primary pickup and drop locations for cab riders in New York City. In an effort to minimize travel time and improve customer service and the utilization of the
The five nodes in the following network represent points one year apart over a four-year period. Each node indicates a time when a decision is made to keep or replace a firmâ€™s computer
The northâ€“south highway system passing through Albany, New York, can accommodate the capacities shown.Can the highway system accommodate a northâ€“south flow of 10,000 vehicles perhour?
If the Albany highway system has revised flow capacities as shown in the following network, what is the maximal flow in vehicles per hour through the system? How many vehicles per hour must travel

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