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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

The following table exhibits the monthly rate of return of S&P 500 and American Express. Use the MINITAB program to:(a) Calculate the mean and standard deviation of both returns.(b) Calculate the
A production process produces 0.05 % defective parts. A sample of 10,000 parts from the production is selected. In(a) and (b), what is the probability that:(a) The sample contains exactly two
The results of a survey of married couples and the number of children they had are shown below.Determine the expected number of children and the standard deviation for the number of children. Number
The average number of calls received by an operator in a 30-min period is 12.(a) What is the probability that between 17:00 and 17:30 the operator will receive exactly eight calls?(b) What is the
In a lot of 200 parts, 50 of them are defective. Suppose a sample of 10 parts is selected at random, what is the probability that two of them are defective? What is the expected number of defective
A study indicates that an assembly line task should take an average of 3.20 min to complete, with a standard deviation of 0.75 min. What is the probability that the task will take between 1.80 and
Indicate whether each of the following random variables is continuous or discrete.(a) The time it takes a mechanic to service a car.(b) The number of new housing starts in New Jersey this year.(c)
The random variable Z is normally distributed with a mean of μz = 0 and a standard deviation of σz = 1. Find the following probabilities: (a) P(Z 1.65) (b) P(Z> -2.38) (c) P(Z> 2.95) (d) P(Z <
The random variable Z is normally distributed with μz = 0 and σz = 1. Find the following values of b: (a) P(Z < b) = .9280 (b) P(Z b) = .9949 (c) P(Z> b) = .0074 (d) P(Z
A random variable X is normally distributed with μX = 5 and σX = 2.7. Find the following probabilities, using both manual calculations and the MINITAB program: (a) P(X < 7.40) (b) P(X> -1.50)
The random variable Y is normally distributed with μY = 28.00 and σY = 10.Find the following values of b: (a) P(Y b) = .8106 (c) P(Y> b) = .0099 (d) P(Y
The following table gives the amount of time X, in seconds, by which an automated manufacturing process misses the designed completion time when performing a certain task. Negative values indicate
Suppose that 35 % of the employees of the Harrison Company belong to unions. To determine union members’ attitudes toward management, the company’s personnel manager takes a random sample of 100
Suppose that a batch of n = 80 items is taken from a manufacturing process that produces a fraction p = .16 of defectives. What is the probability that this batch will contain between 19 and 20
The IQ scores of human beings are scaled to follow a normal distribution with mean 100 and standard deviation 16. If those with IQ scores higher than 154 are regarded as geniuses, how many geniuses
A college professor teaches corporate finance every semester. The tests for the course are standardized so that the test scores exhibit a normal distribution with a mean of 75 and a standard
Suppose that X represents the number of cars arriving at a toll booth in 1 min.Further, suppose that X can assume the values 1, 2, 3, 4, and 5 and has the following distribution:Calculate the
The manager in the local bank discovers that people come in to cash their paychecks on Friday. The amount of money withdrawn on Friday follows a normal distribution with 5 million as the mean and 1
A local bakery found that it was throwing out too many cookies every night, so the manager conducted a study on the sales of cookies and found that on an ordinary day, the sales of cookies follow a
A soft drink producer has just installed a new assembly line. The assembly line is adjusted to dispense an average of 12.05 oz of soda into the 12-oz soda can with a standard deviation of .02. What
In question 17, what is the probability that 2 cans out of a six pack will contain less than 12 oz?Question 17A soft drink producer has just installed a new assembly line. The assembly line is
In question 17, the average amount of soda dispensed into the cans is adjustable. If we want to make sure that 99.9 % of the soda cans contain more than 12 oz, to what should we adjust the
A golfer enters a long-driving contest in which he wins if he drives the golf ball 300 yards or more and loses if he drives it less than 300 yards. Assume that every time he hits a golf ball, he has
A phone marketing company knows that the number of people who answer the phone between 10:00 and 10:15 a.m. has a Poisson distribution. The average number is eight. What is the probability that the
A market survey shows that 75 % of all households own a VCR. Suppose 100 households are surveyed.(a) What is the probability that none of the households surveyed owns a VCR?(b) What is the
You are given the following information about a stock:Calculate the value of the call option if the stock goes up in 3 out of the 5 months. S = $100 X = $101 r = .005 n = 5 u= 1.10 d = .95 Price of
Answer question 57 when u = 1.20. How does a change in the amount of increase if the stock goes up affect the value of the call option?Question 57You are given the following information about a
Answer question 57 when d = .85. How does a change in the amount of decrease if the stock goes down affect the value of the call option?Question 57You are given the following information about a
What is the Poisson distribution? Give some examples of situations wherein it would be appropriate to use the Poisson distribution. Compare the Poisson approximation to the binomial distribution.
What is a Bernoulli trial? Give some examples of a Bernoulli trial related to the binomial distribution.
Using the information from question 43, compute the probability that the stock will go up in at least 7 months during the year.Question 43An analyst calculates the probability of McGregor stock going
An analyst calculates the probability of McGregor stock going up in value for any month as .6 and the probability of the same stock going down in any month as .4. Calculate the probability that the
Tell whether each of the following is a discrete or a continuous random variable:(a) The number of beers sold at a bar during a particular week(b) The length of time it takes a person to drive 50
What is a random variable? What is a discrete random variable? What is a continuous random variable? Give some examples of discrete random variables.
Consider a single toss of a fair coin, and define X as the number of heads that come up on that toss. Then X can be 0 or 1, with a probability of 50 %.The expected value of X is 1/2 . Can we
Suppose that of 40 salespersons in a company, 10 are females and the rest males. Five of them are randomly chosen to attend a seminar. What is the probability that three females and two males are
An insurance company found that one of 5,000 50-year-old, nonsmoking males will suffer a heart attack in a given year. The company has 50,000 50-year-old, nonsmoking male policyholders. What is the
A soft drink company argues that its new cola is the favorite soft drink of the next generation. Ten teenagers were picked to test-drink the cola one by one.Assume that five of them liked the new
After assembly, a finished TV is left turned on for one full day (24 h) to determine whether the product is reliable. On average, two TVs break down each day. Yesterday 500 TVs were produced. What is
Of seven prominent financial analysts who are attending a meeting, three are pessimistic about the future of the stock market, and four are optimistic. A newspaper reporter interviews two of the
In question 32, what is the probability that there are no traffic accidents in all five workdays of a week?Question 32The state highway bureau found that during the rush hour, in the treacherous
The state highway bureau found that during the rush hour, in the treacherous section of a highway, an average of three accidents occur. The probability of there being an accident follows a Poisson
A factory examines its work injury history and discovers that the chance of there being an accident on a given workday follows a Poisson distribution. The average number of injuries per workday is
Billings Company is considering leasing a computer for the next 3 years. Two computers are available. The net present value of leasing each computer in the next 3 years, under different business
In a certain statistics course, the misguided professor is very lenient. He fails about 1 % of the students in the class. Assume that the probability of failing the course follows a Poisson
The makers of two kinds of cola are having a contest in the local shopping mall.Assume that 60 % of the people in this region prefer brand A and 40 % prefer brand B. Ten local residents were randomly
A company found that on average, on a given day, .5 % of its employees call in sick. Assume a Poisson distribution. What is the probability that fewer than two of 300 employees will call in sick?
In the game of roulette, a gambler who wins the bet receives $36 for every dollar she or he bet. A gambler who does not win receives nothing. If the gambler bets $1, what is the expected value of the
There are 38 numbers in the game of roulette. They are 00, 0, 1, 2, . . ., 36. Each number has an equal chance of being selected. In the game, the winning number is found by a spin of the wheel. Say
A medical report shows that 5% of stock brokers suffer stress and need medical attention. There are 10 brokers working for your brokerage house. What is the probability that three of them will need
Despite your discomfort with statistics, you find yourself employed by a dog food manufacturer to do statistical research for quality control purposes. Your job is to weigh the dog food to determine
Returning to question 21, say (1), your company’s policy is to accept the shipment only when fewer than two springs (out of 400 springs examined) are bad, and (2) the proportion of the bad springs
Every week a truckload of springs is delivered to the warehouse you supervise. Every time the springs arrive, you have to measure the strength of 400 springs. You accept the shipment only when there
The local bank manager has found that one out of every 400 bank loans end up in default. Last year the bank made 400 loans. What is the probability that two bank loans will end up in default?
During each hour, 0.1 % of the total production of paperclips is defective. For a random sample of 500 pieces of the product, what is the chance of finding more than one defective item?
An average of three small businesses go bankrupt each month. What is the probability that five small businesses will go bankrupt in a certain month?
A hospital has three doctors working on the night shift. These doctors can handle only three emergency cases in a time period of 30 min. On average, 1/2 an emergency case arises in each 30-min
A student takes an exam that consists of 10 multiple-choice questions. Each question has five possible answers. Suppose the student knows nothing about the subject and just guesses the answer on each
A certain insurance salesman sees an average of five customers in a week. Each time he speaks to a customer, he has a 30 % chance of making a deal. What is the probability that he makes five deals
A baseball player usually has four at bats each game. Suppose the baseball player is a lifetime 0.25 hitter. Find the probability that this player will have:(a) Two hits out of four at bats(b) No
Two teams are playing each other in seven basketball games. Team A is considered to have a 60–40 % edge over team B. What is the probability that team A will win four or more games?
The Wicker company has one repair specialist who services 200 machines in the shop and repairs machines that break down. The average breakdown rate is λ = .5 machine per day (or 1 breakdown every 2
The number of people arriving at a bank teller’s window is Poisson distributed with a mean rate of .75 persons per minute. What is the probability that two or fewer people will arrive in the next 6
A survey was conducted. Of 20 questionnaires that were sent, 12 were completed and returned. We know that 8 of the 20 questionnaires were sent to students and 12 to nonstudents. Only two of the
Consider a group of 12 employees of whom five are in management and seven do clerical work. Select at random a sample of size 4. What is the probability that there will be one manager in this sample?
A fair coin is tossed eight times.(a) Use MINITAB to construct a probability function table.(b) What is the probability that you will have exactly four heads?
A fair die is rolled 10 times. An “ace” means to roll a “6.” Find the probability of getting exactly four aces, of getting five aces, of getting six aces, and of getting four aces or more.
Find the mean and standard deviation of the number of successes in binomial distributions characterized as follows: (a) n = 20, p =.5 (b) n = 100, p = .09 (c) n = 30, p = .7 (d) n = 50, p = 4
The rate of defective items in a production process is 15 %. Assume a random sample of 10 items is drawn from the process. Find the probability that two of them are “defective”. Calculate the
The following table gives the probability distribution for two random variables:x, which measures the total number of times a person will be ill during a year, and y, the sex of this person, where 1
The following table gives the number of unpainted machines in a container.Calculate the mean and standard deviation. Unpainted Probability 0 .05 1 .09 2 .15 3 .30 4 .25 5 .10 6 .05 7 .01
An investment banker estimates the following probability distribution for the earnings per share (EPS) of a firm.Calculate the expected value of the EPS. x(EPS) P(x) 2.25 .05 2.50 .10 2.75 .20 3.00
A team of students participates in a project. The results show that all students are able to finish the project in 7 days. The distribution for the finishing time is given in the following
As controller of the Hamby Corporation, you are directed by the chairman of the board to investigate the problem of overspending by employees who have expense accounts. You ask the accounting
Suppose you are dealing with problems in probability and statistical inference.Which is usually the larger value in the problem, the population size or the sample size? Why?
State which type of statistical problem (deductive or inductive) makes each of the following assumptions.(a) You know what the population characteristics are.(b) You know what the sample
When a cosmetic manufacturer tests the market to determine how many women will buy eyeliner that has been tested for safety without subjecting animals to injury, is it involved in a descriptive
A teacher has just given an algebra exam. What are some of the statistics she could compute?
A bullet manufacturer would like to keep the number of duds (bullets that won’t fire) to a maximum of 2 per box of 100. Should inferential or descriptive statistics be used to decide this issue?
Explain why election pollsters use inferential statistics rather than descriptive statistics to predict the outcome of an election.
Explain whether each of the following was arrived at via descriptive or inferential statistics.(a) Ted Williams’ lifetime batting average(b) The number of people watching the Super Bowl, based on
Suppose you are interested in purchasing AT&T stock. You know that AT&T stock has had an average rate of return of 8 % over the last 5 years. Explain how you could use descriptive statistics to help
Use the information given in the accompanying figure to answer the following questions.(a) Which month has the greatest amount of help-wanted advertising?(b) How did help-wanted advertising fluctuate
A popular commercial claims that “Four out of five dentists prefer sugarless gum.” Is this conclusion drawn from a sample or a population?
The most commonly reported indicator of stock market performance is the Dow Jones Industrial Average. Explain whether the firms whose share price are included in the DJIA represent a sample or a
Suppose a Gallup poll is to be conducted to predict the outcome of the 1992 presidential election. Should the pollsters survey a sample or a population?
If managers at Weight Watchers are interested in the average number of pounds that people on Weight Watchers diets lose, should they use a sample or the population to find out?
Refer to Table 2.2, in which annual macroeconomic data including GDP, CPI, 3-month T-bill rate, prime rate, private consumption, private investment, net exports, and government expenditures from 1960
The following list gives the seven highest-paid baseball players for 1992 and their salaries.(a) Does this list represent a sample or population of baseball players’ salaries?(b) If you were the
Suppose Greg Norman has the following scores in his last eight rounds of golf:71, 68, 64, 73, 69, 62, 75, 69.(a) If Greg computed his average score over these eight rounds, would he be computing a
J. D. Power is a consulting firm that assesses consumer satisfaction for the auto industry. Do you think this company uses a sample or the population to conduct its survey?
Refer to Table 2.2, which of the variables are qualitative and which are quantitative variables?Table 2.2 3-month T-bill Prime Private Private Net Goverment rate consumption investment exports
You are given the following information about a certain company’s current assets over the past 4 years:Use a component-lines graph to plot this firm’s current assets. Current assets Cash and
Briefly explain why learning statistical inference is important for students of business and economics. Give two examples.
Define the term statistics. What are the two basic types of statistics? Describe them and give examples.
Explain the difference between deductive and inductive statistics. Illustrate your answer with examples taken from everyday life.
You are assigned by your general manager to examine each of last month’s sales transactions. Find their average, find the difference between the highest and lowest sates figures, and construct a
Using any newspaper of your choice, find examples of statistics from the following sections:(a) Sports section(b) Business section(c) Entertainment section
The owner of a factory regularly requests a graphical summary of all employees’ salaries. The graphical summary of salaries is an example of descriptive statistics inferential statistics?
Of 354 MBA students, the following numbers chose to concentrate their study in these fields: 35 in finance, 63 in accounting, 70 in marketing, 35 in operations management, 52 in management

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