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Questions and Answers of
Statistics
Consider the following mixed-integer linear program: Max 2x1 + 3x2 s.t. 4x1 + 9x2 ( 36 7x1 + 5x2 ( 35 x1, x2 ( 0 and x1 integer a. Graph the constraints for this problem. Indicate on your graph all
The purpose of this exercise is to provide practice using LINGO or Excel Solver. Find the values of X and Y that minimize the function Min X2 - 4X + Y2 + 8Y + 20 Do not assume non-negativity of the X
Using the return data in Table 12.10, construct a portfolio from Apple, AMD, and Oracle that matches the Information Technology S&P index as closely as possible. Use the return data for the
Larosa Job Shop is studying where to locate its tool bin facility on the shop floor. There are five production cells (fabrication, paint, subassembly 1, subassembly 2, and assembly) at fixed
Many people regard video games as an obsession for youngsters, but, in fact, the average age of a video game player is 35 years (Reuters.com, August 21, 2009). Is the value 35 likely the actual or
Annual sales at a small pharmaceutical firm have been rather stagnant over the most recent five-year period, exhibiting only 1.2% growth over this time frame. A research analyst prepares the
Construct a scatterplot with the following data. Categorize the relationship between x and y.
Patrons at a local restaurant were asked to rate their recent experience at the restaurant with respect to its advertised atmosphere of upbeat, comfortable, and clean. Possible responses included
The following table reports the number of people as well as the number of people living below the poverty level across regions in the U.S. for the year 2013. (All numbers are in 1,000s.)a. Construct
There are six broad sectors that comprise the Dow Jones Industrial Average (DJIA). These are the broad areas in which the company conducts business. The following table shows a list of the 30
Calculate the average growth rate return for the following data set: 4% ......8% ......-5% ......6%
The returns for a pharmaceutical firm are 10% in Year 1, 5% in Year 2, and -15% in Year 3. What is the annualized return for the period?
The returns from an investment are 2% in Year 1, 5% in Year 2, and 1.8% in the first half of Year 3. Calculate the annualized return for the entire period.
The returns for an auto firm are 5% in Year 1 and 3% in the first quarter of Year 2. Calculate the annualized return for the period.
Consider the following observations for a series: Year 1......Year 2.........Year 3..........Year 4 90...................110.............150...............160 a. Calculate the growth rates for Year
Consider the following observations for a time series: Year 1..........Year 2..........Year 3..........Year 4 1,200............1,280............1,380...........1,520 a. Calculate the growth rates for
Suppose at the beginning of 2006 you decide to invest $1,000 in Vanguard's European Stock Index mutual fund. The following table shows the returns for the years 2006-2009. Year Annual
Home Depot and Lowe's are the two largest home improvement retailers in the U.S. The following table shows the total revenue (in billions) for each retailer for the years 2008-2010.Source: Annual
Suppose at the beginning of 2005 you decide to invest $20,000 in Driehaus' Emerging Markets Growth mutual fund. The following table shows the returns for the years
The following table shows the total revenue (in billions of $) for Walmart Stores, Inc. and Target Corp. for the years
The following table shows sales for Nike (in millions of $) for the years 2005 through
Real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 24, 2010). Marcela Treisman works for an investment firm in Michigan. Her assignment is
The accompanying data file shows the Fortune 500 rankings of America's largest corporations for 2010. Next to each corporation are its market capitalization (in billions of dollars as of March 26,
The accompanying data file shows, among other variables, median household income and median house value for the 50 states. a. Compute and discuss the range of household income and house value. b.
The following table shows the revenues (in millions of dollars) for The Gap, Inc., and American Eagle Outfitters, Inc., for the years 2008-2010. Source: Annual Reports for Gap, Inc., and American
On Sunday, July 11, 2010, Spain and the Netherlands played in the 2010 World Cup Final in Johannesburg. On the eve of the final, many betting lines were offering Spain's odds for winning at 15:8
Prior to the Academy Awards ceremony in 2009, the United Kingdom bookmaker Ladbrokes reported the following odds for winning an Oscar in the category of best actress (The Wall Street Journal,
Let P(A) = 0.65, P(B) = 0.30, and P(A | B) = 0.45. a. Calculate P(A ∩ B). b. Calculate P(A ∪ B). c. Calculate P(B | A).
Let P(A) = 0.55, P(B) = 0.30, and P(A ∩ B) = 0.10. a. Calculate P (A | B). b. Calculate P (A ∪ B). c. Calculate P ((A ∪ B)c).
Express each of the probabilities in the preceding question asa. Odds assessed by Sunil for obtaining tails.b. Odds assessed by John for receiving straight A's.c. Odds assessed by the reporter for a
Only 20% of students in a college ever go to their professor during office hours. Of those who go, 30% seek minor clarification and 70% seek major clarification. a. What is the probability that a
Complete the following probability table.
Complete the following probability table.
Calculate the following values. a. 8! and 6! b. 8C6 c. 8P6
Calculate the following values. a. 7! and 3! b. 7C3 c. 7P3
Twenty cancer patients volunteer for a clinical trial. Ten of the patients will receive a placebo and 10 will receive the trial drug. In how many different ways can the researchers select 10 patients
There are 10 players on the local basketball team. The coach decides to randomly pick 5 players for the game. a. In how many different ways can the coach select 5 players to start the game if order
A horse-racing fan is contemplating the many different outcomes in an eight-horse race. a. How many different combinations are possible if only the first three places (first, second, and third) are
David Barnes and his fiancée Valerie Shah are visiting Hawaii. At the Hawaiian Cultural Center in Honolulu, they are told that 2 out of a group of 8 people will be randomly picked for a free
AccuScore calculated an 84% chance that there would be a fight during the game between theAnaheim Ducks and the Chicago Blackhawks, two of the National Hockey League's most pugnacious teams (The Wall
The Easy Credit Company reports the following table representing a breakdown of customers according to the amount they owe and whether a cash advance has been made. An auditor randomly selects one of
A recent study shows that unemployment does not impact males and females in the same way (Newsweek, April 20, 2009). According to a Bureau of Labor Statistics report, 8.5% of those who are eligible
Prior to the start of the season, a sports analyst is attempting to predict the end-of-season rankings of the 10 teams in a conference. a. How many different ways can the teams be ranked if ties are
Assume high school coach Emily Williams has seven possible swimmers for a four-person relay team. a. If the order for the freestyle relay is unimportant, how many different relay teams are
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution.
Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution.
What are the portfolio weights for a portfolio that has 100 shares of Stock X that sell for $20 per share and 200 shares of Stock Y that sell for $12 per share?
A portfolio has $200,000 invested in Asset X and $300,000 in Asset Y. Consider the summary measures in the following table. Measures Asset X Asset Y Expected Return
An analyst has predicted the following returns for Stock A and Stock B in three possible states of the
A pension fund manager is considering three mutual funds for investment. The first one is a stock fund, the second is a bond fund and the third is a money market fund. The money market fund yields a
You have $400,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $200,000. Consider the summary measures in the following table: Investment Expected
An investor owns a portfolio consisting of two mutual funds, A and B, with 35% invested in A. The following table lists the inputs for these funds.Measures
An estimated 1.8 million students take on student loans to pay ever-rising tuition and room and board (The New York Times, April 17, 2009). It is also known that the average cumulative debt of recent
Compute the mean and the variance of a lognormal variable Y = eX where X is normally distributed with the following mean and variance: a. μ = 3, σ2 = 2 b. μ = 5, σ2 = 2 c. μ = 5, σ2 = 3
Let Y = eX, where X is normally distributed. Compute the mean and the variance of X given the following information. a. μY = 14, σ2Y = 22 b. μY = 20, σ2Y =22 c. μY = 20, σ2Y =120
Let Y = eX where X is normally distributed with μ = 1.8 and σ = 0.80. Compute the following values. a. P(Y ≤ 7.5) b. P (8 < Y < 9) c. The 90th percentile of Y
Let Y have the lognormal distribution with mean 82.8 and variance 156.25. Compute the following probabilities.a. P (Y > 100)b. P (80 < Y < 100)
The Bahamas is a tropical paradise made up of 700 islands sprinkled over 100,000 square miles of the Atlantic Ocean. According to the figures released by the government of the Bahamas, the mean
It is well documented that a typical washing machine can last anywhere between 5 to 12 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX where X is normally
The relief time provided by a standard dose of a popular children's allergy medicine averages six hours with a standard deviation of two hours.a. Determine the percentage of children who experience
Vanguard's Precious Metals and Mining fund (Metals) and Fidelity's Strategic Income fund (Income) were two top-performing mutual funds for the years 2000 through 2009. An analysis of annual return
Following customer complaints about the quality of service, Dell stopped routing corporate customers to a technical support call center in Bangalore, India (USA TODAY, November 24, 2003). Suppose
A study reports that recent college graduates from New Hampshire face the highest average debt of $31,048 (The Boston Globe, May 27, 2012). A researcher from Connecticut wants to determine how recent
The following table shows the annual returns (in percent) for Fidelity's Electronics and Utilities funds. Year Electronics
The following table shows the annual returns (in percent) for the Vanguard Energy
Real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 24, 2010). Marcela Treisman works for an investment firm in Michigan. Her assignment is
The data accompanying this exercise show the weekly stock price for Home Depot. Assume that stock prices are normally distributed with a population standard deviation of $3. a. State the null and the
Consider the following data drawn independently from normally distributed populations: x1 = 25.7 x2 = 30.6 σ12 = 98.2 σ22 = 87.4 n1 = 20 n2 = 25 a. Construct the 95% confidence interval for the
An entrepreneur owns some land that he wishes to develop. He identifies two development options: build condominiums or build apartment buildings. Accordingly, he reviews public records and derives
A design engineer at Sperling Manufacturing, a supplier of high-quality ball bearings, claims a new machining process can result in a higher daily output rate. Accordingly, the production group is
"The See Me" marketing agency wants to determine if time of day for a television advertisement influences website searches for a product. They have extracted the number of website searches occurring
Consider the following data drawn independently from normally distributed populations: x1 = -10.5 x2 = -16.8 s12 = 7.9 s22 = 9.3 n1 = 15 n2 = 20 a. Construct the 95% confidence interval for the
The production department at Greenside Corporation, a manufacturer of lawn equipment, has devised a new manual assembly method for its lawn tractors. Now it wishes to determine if it is reasonable to
Recent evidence suggests that graduating from college during bad economic times can impact the graduate's earning power for a long time (Financial Times, June 1, 2012). An associate dean at a
The quality department at Electro Tech is examining which of two microscope brands (Brand A or Brand B) to purchase. They have hired someone to inspect six circuit boards using both microscopes.
A computer technology firm wishes to check whether the speed of a new processor exceeds that of an existing processor when used in one of its popular laptop computer models. Accordingly, it measures
The marketing department at Insure-Me, a large insurance company, wants to advertise that customers can save, on average, more than $100 on their annual automotive insurance policies (relative to
The labor quotation department at Excabar, a large manufacturing company, wants to verify the accuracy of their labor bidding process (estimated cost per unit versus actual cost per unit). They have
Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-flooring manufacturing company. Accordingly, engineers at Lumber works are investigating a potential new
The director of housekeeping at Elegante, a luxury resort hotel with two locations (Seaside and Oceanfront), wants to evaluate housekeeping performance at those two locations. Random samples of 100
Due to late delivery problems with an existing supplier, the director of procurement at Electro Tech began to place orders for electrical switches with a new supplier as part of a "dual-source"
Find the value x for which: a. P (χ28 ≥ x) = 0.025 b. P (χ28 ≥ x) = 0.05 c. P (χ28 < x) = 0.025 d. P (χ28 < x) = 0.05
A replacement part for a machine must be produced within close specifications in order for it to be acceptable to customers. A random sample of 20 parts drawn from a normally distributed population
A consumer advocacy group is concerned about the variability in the cost of prescription medication. The group surveys eight local pharmacies and obtains the following prices for a particular brand
The following table shows the annual returns (in percent) for the Vanguard Energy Fund from 2005 through
The manager of a supermarket would like the variance of the waiting times of the customers not to exceed 3 minutes squared. She would add a new cash register if the variance exceeds this threshold.
A restaurant owner is concerned about the consistency of business. He wants to determine if the standard deviation of the profits for each week is less than $300. The profits from last week are
India Fund, Inc. (IFN) is a close-ended equity mutual fund launched by the Blackstone Group, Asset Management Arm. Although it promises impressive returns, it does so at the cost of greater risk. An
Metal works, a supplier of machine parts, fabricates bearings for use in aeronautical applications in which the standard deviation of the bearing diameter must be within 0.002 inch maximum.
Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical factor in determining the likelihood of an accident occurring (Update,
To maintain high consistency in its manual sewing operations, a custom manufacturer of high-quality fashion clothing has a goal in which all sewing employees should score within a standard deviation
An economist is interested in the variability of hourly wages at a production plant. She collects data on 50 hourly wage earners. a. Set up the competing hypotheses to test whether the variance of
Find the value x for which: a. P ( χ220 ≥ x) = 0.005 b. P( χ220 ≥ x) = 0.01 c. P( χ220 < x) = 0.005 d. P( χ220 < x) = 0.01
A realtor in Mission Viejo, California, believes that the standard deviation of house prices is more than 100 units, where each unit equals $1,000. Assume house prices are normally distributed.a.
The data accompanying this exercise show miles per gallon (mpg) for 25 cars. a. State the null and the alternative hypotheses in order to test whether the variance differs from 62 mpg2. b. Assuming
Real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 24, 2010). With rents holding up, this is good news for investors but the same cannot be
Find the value x for which: a. P (F(4,8) ≥ x) = 0.025 b. P(F(4,8) ≥ x) = 0.05 c. P(F(4,8) < x) = 0.025 d. P(F F(4,8) < x) = 0.05
Use the F table to approximate the following probabilities. a. P (F(10,8) ≥ 3.35) b. P (F(10,8) < 0.42) c. P (F (10,8) ≥ 4.30) d. P (F(10,8) < 0.26)
Construct the 90% interval estimate for the ratio of the population variances using the following results from two independently drawn samples from normally distributed populations. Sample 1: 1 =
Consider the following measures based on independently drawn samples from normally distributed populations: Sample 1: s21 = 220, and n1 = 20 Sample 2: s2 2 = 196, and n2 = 15 a. Construct the 95%
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