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statistics

Questions and Answers of Statistics

Consumer demand for small, economical automobiles depends somewhat on recent trends in the average price of unleaded gasoline. For example, consider the information given in the file S04_26.xlsx on
Upon completing their respective homework assignments, marketing majors and accounting majors at a large state university enjoy hanging out at the local tavern in the evenings. The file S04_27.xlsx
Let X and Y represent the number of Dell and HP laptop computers, respectively, sold per month from online sites. The file S04_28.xlsx contains the probabilities of various combinations of monthly
The joint probability distribution of the weekly demand for two brands of diet soda is provided in the file S04_29.xlsx. In particular, let D1 and D2 represent the weekly demand (in hundreds of
A local pharmacy has two checkout stations available to its customers: a regular checkout station and an express checkout station. Customers with six or fewer items are assumed to join the express
Suppose that the manufacturer of a particular product assesses the joint distribution of price P per unit and demand D for its product in the coming quarter as provided in the file S04_31.xlsx.a.
The recent weekly trends of two particular stock prices can best be described by the joint probability distribution shown in the file S04_32.xlsx.a. What is the probability that the price of stock 1
Two service elevators are used in parallel by employees of a three-story hotel building. At any point in time when both elevators are stationary, let X1 and X2 be the floor numbers at which elevators
The file S04_34.xlsx shows the conditional distribution of the daily number of accidents at a given intersection during the winter months, X2, given the amount of snowfall (in inches) for the day,
A sporting goods store sells two competing brands of exercise bicycles. Let X1 and X2 be the numbers of the two brands sold on a typical day at this store. Based on available historical data, the
The file P04_28.xlsx contains the probabilities of various combinations of monthly sales volumes of Dell (X) and HP (Y) laptop computers from online sites. Are the monthly sales of these two
Let D1 and D2 represent the weekly demand (in hundreds of two-liter bottles) for brand 1 diet soda and brand 2 diet soda, respectively, in a small central Indiana town. The joint probability
The file S04_31.xlsx contains the joint probability distribution of price P per unit and demand D for a particular product in the coming quarter.a. Are P and D independent random variables? Explain
You know that in one year you are going to buy a house. The annual interest rate for fixed-rate 30-year mortgages is currently 6.00%, and the price of the type of house you are considering is
A typical consumer buys a random number (X) of polo shirts when he shops at a men’s clothing store. The distribution of X is given by the following probability distribution: P(X = 0) = 0.30, P(X =
Based on past experience, the number of customers who arrive at a local gasoline station during the noon hour to purchase fuel is best described by the probability distribution given in the file
Let X be the number of defective items found by a quality inspector in a random batch of 15 items from a particular manufacturing process. The probability distribution of X is provided in the file
The probability distribution for the number of job applications processed at a small employment agency during a typical week is given in the file S04_43.xlsx. a. Assuming that it takes the agency’s
Consider a financial services salesperson whose annual salary consists of both a fixed portion of $25,000 and a variable portion that is a commission based on her sales performance. In particular,
A film-processing shop charges its customers 18 cents per print, but customers may refuse to accept one or more of the prints for various reasons. Assume that this shop does not charge its customers
Suppose the monthly demand for Thomson televisions has a mean of 40,000 and a standard deviation of 20,000. Find the mean and standard deviation of the annual demand for Thomson TVs. Assume that
Suppose there are five stocks available for investment and each has an annual mean return of 10% and a standard deviation of 4%. Assume the returns on the stocks are independent random variables.a.
An investor puts $10,000 into each of four stocks, labeled A, B, C, and D. The file S04_48.xlsx contains the means and standard deviations of the annual returns of these four stocks. Assuming that
Consider again the investment problem described in the previous problem. Now, assume that the returns of the four stocks are no longer independent. Specifically, the correlations between all pairs of
A supermarket chain operates five stores of varying sizes in Bloomington, Indiana. Profits (represented as a percentage of sales volume) earned by these five stores are 2.75%, 3%, 3.5%, 4.25%, and
A manufacturing company constructs a 1-cm assembly by snapping together four parts that average 0.25 cm in length. The company would like the standard deviation of the length of the assembly to be
The weekly demand function for one of a given firm’s products can be represented by q = 200 - 5p, where q is the number of units purchased (in hundreds) at price p (in dollars). Assume that the
A retailer purchases a batch of 1000 fluorescent light bulbs from a wholesaler at a cost of $2 per bulb. The wholesaler agrees to replace each defective bulb with one that is guaranteed to function
A business manager who needs to make many phone calls has estimated that when she calls a client, the probability that she will reach the client right away is 60%. If she does not reach the client on
Suppose that a marketing research firm sends questionnaires to two different companies. Based on historical evidence, the marketing research firm believes that each company, independently of the
Based on past sales experience, an appliance store stocks five window air conditioner units for the coming week. No orders for additional air conditioners will be made until next week. The weekly
Simulate 1000 weekly consumer demands for window air conditioner units with the probability distribution given in the file S04_56.xlsx. How does your simulated distribution compare to the given
The probability distribution of the weekly demand for copier paper (in hundreds of reams) used in the duplicating center of a corporation is provided in the file S04_58.xlsx.a. Find the mean and
Consider the probability distribution of the weekly demand for copier paper (in hundreds of reams) used in a corporation’s duplicating center, as shown in the file S04_58.xlsx.a. Use simulation to
The probability distribution of the weekly demand for copier paper (in hundreds of reams) used in the duplicating center of a corporation is provided in the file S04_58.xlsx. Assuming that it costs
The instructor of an introductory organizational behavior course believes that there might be a relationship between the number of writing assignments (X) she gives in the course and the final grades
The file S04_62.xlsx contains the joint probability distribution of recent weekly trends of two particular stock prices, P1 and P2.a. Are P1 and P2 independent random variables? Explain why or why
Consider two service elevators used in parallel by employees of a three-story hotel building. At any point in time when both elevators are stationary, let X1 and X2 be the floor numbers at which
A roulette wheel contains the numbers 0, 00, and 1 to 36. If you bet $1 on a single number coming up, you earn $35 if the number comes up and lose $1 otherwise. Find the mean and standard deviation
Assume that there are four equally likely states of the economy: boom, low growth, recession, and depression. Also, assume that the percentage annual return you obtain when you invest a dollar in
Suppose there are three states of the economy: boom, moderate growth, and recession. The annual return on Honda and Toyota stock in each state of the economy is shown in the file S04_66.xlsx.a.
Each year the employees at Zipco receive a $0, $2000, or $4500 salary increase. They also receive a merit rating of 0, 1, 2, or 3, with 3 indicating outstanding performance and 0 indicating poor
The return on a portfolio during a period is defined by PVend – Pvbeg / PVbegWhere PVbeg is the portfolio value at the beginning of a period and PVend is the portfolio value at the end of the
You are involved in a risky business venture where three outcomes are possible: (1) You will lose not only your initial investment ($5000) but an additional $3000; (2) You will just make back your
Suppose X and Y are independent random variables. The possible values of X are -1, 0, and 1; the possible values of Y are 10, 20, and 30. You are given that P(X = -1 and Y = 10) = 0.05, P(X = 0 and Y
Equation (4.7) for variance indicates exactly what variance is: the weighted average of squared deviations from the mean, weighted by the probabilities. However, the computing formula for variance,
Equation (4.10) for covariance indicates exactly what covariance is: the weighted average of products of deviations from the means, weighted by the joint probabilities. However, the computing formula
The basic game of craps works as follows. You throw two dice. If the sum of the two faces showing up is 7 or 11, you win and the game is over. If the sum is 2, 3, or 12, you lose and the game is
Imagine that you are trying to predict the price of gasoline (regular unleaded) and the price of natural gas for home heating during the next month. Assume you believe that the price of either will
Consider an individual selected at random from a sample of 750 married women in answering each of the following questions.a. What is the probability that this woman does not work outside the home,
Suppose that 8% of all managers in a given company are African American, 13% are women, and 17% have earned an MBA degree from a top-10 graduate business school. Let A, B, and C is, respectively, the
Consider again the supermarket chain described in Problem 50. Now, assume that the daily sales of the five stores are no longer independent of one another. In particular, the file S04_77.xlsx
A manufacturing plant produces two distinct products, A and B. The cost of producing one unit of A is $18 and that of B is $22. Assume that this plant incurs a weekly setup cost of $24,000 regardless
The typical standard deviation of the annual return on a stock is 20% and the typical mean return is about 12%. The typical correlation between the annual returns of two stocks is about 0.25. Mutual
You are ordering milk for Mr. D’s supermarket, and you are determined to please. Milk is delivered once a week (at midnight Sunday). The mean and standard deviation of the number of gallons of milk
Two gamblers play a version of roulette with a wheel as shown in the file S04_81.xlsx. Each gambler places four bets, but their strategies are different, as explained below. For each gambler, use the
Suppose the New York Yankees and Philadelphia Phillies are playing a best-of-three series. The first team to win two games is the winner of the series, and the series ends as soon as one team has won
The application at the beginning of this chapter describes the campaign McDonald’s used several years ago, where customers could win various prizes.a. Verify the figures that are given in the
A manufacturing company is trying to decide whether to sign a contract with the government to deliver an instrument to the government no later than eight weeks from now. Due to various uncertainties,
Have you ever watched the odds at a horse race? You might hear that the odds against a given horse winning are 9 to 1, meaning that the horse has a probability 1/(1 + 9) = 1/10 of winning. However,
The results we obtain with conditional probabilities can be quite counterintuitive, even paradoxical. This case is similar to one described in an article by Blyth (1972), and is usually referred to
The grades on the midterm examination given in a large managerial statistics class are normally distributed with mean 75 and standard deviation 9. The instructor of this class wants to assign an A
Suppose it is known that the distribution of purchase amounts by customers entering a popular retail store is approximately normal with mean $25 and standard deviation $8.a. What is the probability
A machine used to regulate the amount of a certain chemical dispensed in the production of a particular type of cough syrup can be set so that it discharges an average of µ milliliters (ml) of the
Assume that the weekly demand for Ford car sales follows a normal distribution with mean 50,000 cars and standard deviation 14,000 cars. a. There is a 1% chance that Ford will sell more than what
An investor has invested in nine different investments. The dollar returns on the different investments are probabilistically independent, and each return follows a normal distribution with mean
Scores on an exam appear to follow a normal distribution with µ = 60 and σ = 20. The instructor wishes to give a grade of D to students scoring between the 10th and 30th percentiles on the exam.
Suppose that the weight of a typical American male follows a normal distribution with µ = 180 lb and σ = 30 lb. Also, suppose 91.92% of all American males weigh more than I weigh.a. What fraction
Assume that the length of a typical televised baseball game, including all the commercial timeouts, is normally distributed with mean 2.45 hours and standard deviation 0.37 hour. Consider a televised
The amount of a soft drink that goes into a typical 12-ounce can varies from can to can. It is normally distributed with an adjustable mean µ and a fixed standard deviation of 0.05 ounce. a. If
Suppose that the demands for a company’s product in weeks 1, 2, and 3 are each normally distributed. The means are 50, 45, and 65. The standard deviations are 10, 5, and 15. Assume that these three
Matthew’s Bakery prepares peanut butter cookies for sale every morning. It costs the bakery $0.50 to bake each peanut butter cookie, and each cookie is sold for $1.25. At the end of the day,
The manufacturer of a particular bicycle model has the following costs associated with the management of this product’s inventory. In particular, the company currently maintains an inventory of
Suppose that a particular production process fills detergent in boxes of a given size. Specifically, this process fills the boxes with an amount of detergent (in ounces) that is adequately described
It is widely known that many drivers on interstate highways in the United States do not observe the posted speed limit. Assume that the actual rates of speed driven by U.S. motorists are normally
The lifetime of a certain manufacturer’s washing machine is normally distributed with mean 4 years. Only 15% of all these washing machines last at least 5 years. What is the standard deviation of
You have been told that the distribution of regular unleaded gasoline prices over all gas stations in Indiana is normally distributed with mean $2.95 and standard deviation $0.075, and you have been
A fast-food restaurant sells hamburgers and chicken sandwiches. On a typical weekday the demand for hamburgers is normally distributed with mean 313 and standard deviation 57; the demand for chicken
Referring to the box plots introduced in Chapter 2, the sides of the “box” are at the first and third quartiles and the difference between these (the length of the box) is called the
In a typical month, an insurance agent presents life insurance plans to 40 potential customers. Historically, one in four such customers chooses to buy life insurance from this agent. Based on the
Continuing the previous exercise, use the normal approximation to the binomial to answer each of the questions posed in parts a through f. How well does the normal approximation perform in this case?
Many vehicles used in space travel are constructed with redundant systems to protect flight crews and their valuable equipment. In other words, backup systems are included within many vehicle
Suppose that a popular hotel for vacationers in Orlando, Florida, has a total of 300 identical rooms. As many major airline companies do, this hotel has adopted an overbooking policy in an effort to
A production process manufactures items with weights that are normally distributed with mean 15 pounds and standard deviation 0.1 pound. An item is considered to be defective if its weight is less
Past experience indicates that 30% of all individuals entering a certain store decide to make a purchase. Using (a) the binomial distribution and (b) the normal approximation to the binomial, find
Suppose that the number of ounces of soda put into a soft-drink can is normally distributed with µ = 12.05 ounces and σ = 0.03 ounce.a. Legally, a can must contain at least 12 ounces of soda. What
Suppose that 53% of all registered voters prefer Barack Obama to John McCain. a. In a random sample of 100 voters, what is the probability that the sample will indicate that Obama will win the
Assume that, on average, 95% of all ticket holders’ show up for a flight. If a plane seats 200 people, how many tickets should be sold to make the chance of an overbooked flight as close as
Suppose that 55% of all people prefer Coke to Pepsi. We randomly choose 500 people and ask them if they prefer Coke to Pepsi. What is the probability that our survey will (erroneously) indicate that
A firm’s office contains 150 PCs. The probability that a given PC will not work on a given day is 0.05. a. On a given day what is the probability that exactly one computer will not be working?b. On
Suppose that 4% of all tax returns are audited. In a group of n tax returns, consider the probability that at most two returns are audited. How large must n be before this probability is less than
Suppose that the height of a typical American female is normally distributed with µ = 64 inches and σ = 4 inches. We observe the height of 500 American females.a. What is the probability that fewer
Consider a large population of shoppers, each of whom spends a certain amount during his or her current shopping trip; the distribution of these amounts is normally distributed with mean $55 and
Many firms utilize sampling plans to control the quality of manufactured items ready for shipment. To illustrate the use of a sampling plan, suppose that a particular company produces and ships
Suppose you play a game at a casino where your probability of winning each game is 0.49. On each game, you bet $10, which you either win or lose. Let P(n) be the probability that you are ahead by at
Comdell Computer receives computer chips from Chipco. Each batch sent by Chipco is inspected as follows: 35 chips are tested and the batch passes inspection if at most one defective chip is found in
A standardized test consists entirely of multiple-choice questions, each with five possible choices. You want to ensure that a student who randomly guesses on each question will obtain an expected
In the current tax year, suppose that 5% of the millions of individual tax returns are fraudulent. That is, they contain errors that were purposely made to cheat the government.a. Although these
Suppose you work for a survey research company. In a typical survey, you mail questionnaires to 150 companies. Of course, some of these companies might decide not to respond. Assume that the
Suppose you are sampling from a large population, and you ask the respondents whether they believe men should be allowed to take paid paternity leave from their jobs when they have a new child. Each

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