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statistics for business and economics

Questions and Answers of Statistics For Business And Economics

What is the probability that at least two students in a class of 20 students will have the same birthday? Assume that there are no twins among the students and that all of the 365 birthdays are
What is the probability of drawing three spades in a row from a standard deck of cards without replacement?
Roll a pair of dice ten times and then calculate the mean and standard deviation for these rolls.(a) What is the largest possible mean?(b) What is the smallest possible mean?(c) What is the smallest
Suppose a bag contains 12 balls distributed as follows: five red dotted balls, two red striped balls, one gray dotted ball, and four gray striped balls.(a) Suppose you draw a red ball from the bag.
Determine the probability of betting on a winning number in a game of roulette.The numbers on the wheel are 0, 00, and 1 through 36. Each number is as likely as any other to become a winning number.
The probability that a car dealer will make a sale when he meets a prospective customer is 20 %. If he meets three customers at random, what is the probability that all three customers will purchase
In a class of ten students, we find that the students spent the following amounts of money on textbooks for the semester:(a) Find the median dollar value spent on books.(b) Find the mean and standard
Reconsider question 57, but this time assume that each population has three members.Question 57Suppose you have three populations containing two members each. Suppose the means and the variances of
Suppose you have three populations containing two members each. Suppose the means and the variances of the three populations are the same. Are the numerical values of the members of the first
Suppose the variance of a population is 0. What can you say about the members of that population?
Compute the mean, standard deviation, and coefficient of variation for NPW and PHS.The following information from Best’s Aggregates and Averages can be used for question. You are given the
If you were interested in comparing the dispersion of NPW to the dispersion of PHS, should you use the variance, the standard deviation, or the coefficient of variation’? Which variable—NPW or
Draw a relative and cumulative relative frequency histogram for NPW and PHS.The following information from Best’s Aggregates and Averages can be used for question. You are given the following
Answer the following questions by referring to the MINITAB output of Ford’s current ratio:(a) Is the frequency histogram of Ford’s current ratio symmetric or skewed?(b) Compare and analyze the
Draw a frequency and cumulative frequency histogram for Chrysler’s inventory turnover. Is this frequency histogram symmetric or skewed?
Compute the mean, variance, and coefficient of variation for Chrysler’s inventory turnover.
You are given the sample space S = {a, b, c, d, e} and the events A = {a, c, e} and B = {b, d, e}. (a) List the events AUB, ANB, A, B, AMB, and (AUB). (b) Draw a Venn diagram for An B.
A bag consists of ten balls, three white and seven red.(a) What is the probability of drawing a white ball?(b) What is the probability of drawing a white ball on the first draw and a red ball on the
A survey of 200 students yields the following data:(a) What is the probability of drawing at random a student who owns both a computer and a TV?(b) What is the probability of drawing at random a
Calculate the probability for scores less than 600. SAT scores for Fiesta University SAT 750-800 700-750 650-700 600-650 550-600 500-550 450-500
In which of the following sets are the two events independent? In which are they mutually exclusive? In which are they neither?(a) The Detroit Pistons win the NBA champion ship and the Oakland A’s
A bag contains three balls: a black one, a white one, and a red one. A magician takes the balls out one by one. Draw an outcome tree. What is the probability of drawing the balls in the order of
Suppose that P(E1) = 0.3 and P(E2) = 0.4. Obtain and P(E UE), PE E),
A baseball player has a lifetime batting average of .3. During a game, he has 5 at bats. A student of statistics argues that his chance of going 5 for 5 is (.3)5.Do you agree? What assumption does
The sales department wants to send two sales representatives on a business trip.There are five women and five men in the department. If the sales manager randomly selects two people, what is the
In question 21, if we draw two students at random without replacement, what is the probability of our getting a student who owns both and a student who owns neither?Question 21A survey of 200
A cereal company runs a certain advertisement in three media: newspaper, radio, and TV. Of the customers surveyed, 40 saw the advertisement on TV, 40 heard it on the radio, 30 read it in the
A city company has 300 employees. Among these employees, two out of every three take public transportation to work, one out of every two owns a car, and one out of every three owns a car but takes
Draw 2 cards from a deck of cards without replacement. What is the probability of getting a diamond on the first draw and a club on the second? What is the probability of drawing 2 cards and getting
What is the probability of getting the same outcome in 2 rolls of a die? What is the probability that the sum of 2 outcomes is 7?
Of the light bulbs delivered on May 25, 400 are produced in the morning shift, 300 in the evening shift, and 300 in the night shift. Say we pick a light bulb at random.(a) What is the probability
In question 27, assume that 1/10 of the light bulbs produced in the morning shift, 1/10 of the light bulbs produced in the evening shift, and 1/5 of the light bulbs produced in the night shift are
The business majors at Metropolitan University can be broken down as follows:(a) We have randomly selected four students to attend a regional conference.What is the probability that we have a
A survey at Metropolitan College shows that among 750 economics majors, every student has taken at least one course in either economics or statistics. We also know that:450 students have taken
A local factory has two shifts: day shift and night shift. The day shift produces 2/3 of the total product. Of the day shift product, 1 % are defective. Of the night shift product, 2 % are defective.
An insurance agent talks to three customers each day. Her probability of making a sale in the first meeting with a customer is .2. When she gets the second meeting with the same customer, the
Three different manuals were used to teach students how to type. Each manual was used by 1/3 of the students. The results show that 30 % of the students using manual A, 20 % of the students using
Fifty percent of the economists in the country are conservatives. The other 50%are liberals. Thirty percent of the conservative economists and 20%of the liberal economists believe that we will have a
A training program is effective for 80 % of the students whose mathematics background is strong, but it is effective for only 60 % whose math background is not good. Assume that only 60 % of a group
A training program is effective for 80 % of the students who are strongly motivated, but it is effective on only 60 % of the students who are not strongly motivated. Assume that only 60 % of the
Three percent of the products produced by the new assembly line are defective.Five percent of the products produced by the old machine are defective. The new machine produced 70 % of the total
Mr. Doe wants to send two employees in his company on a business trip. He has five employees in the company. In how many different ways can he organize the trip?
An advertising agency wanted to find out what kinds of readers subscribed to a sports magazine. The agency sent out questionnaires with the magazine and received the following result:(a) If we know
When playing the Megabucks Lottery, a player is supposed to pick 6 numbers out of 48. If the lottery committee randomly picks the same 6 numbers, then the player hits the jackpot. What is the chance
Define the following terms: event, random experiment, subset, sample space, sample points.
Why is the concept of probability important to understanding statistics?
Explain what we mean when we say two events are independent.
Compare a simple event to a composite event. Give an example of each.
What do we mean by the union of two events? What do we mean by the intersection of two events? Use a Venn diagram to illustrate this point.
Explain what we mean by mutually exclusive events.
Briefly define conditional probability. Give some examples of conditional probability.
What is a joint probability? What is a marginal probability?
What is a prior probability? What is a posterior probability? Briefly explain how Bayes’ theorem can be used to link the two.
What is the probability of obtaining a head in one toss of a fair coin? What is the probability of rolling a 5 in one roll of a fair die? What is the probability of tossing a head and rolling a 5?
You are dealt 4 cards from a standard 52-card deck. What is the probability that you will be dealt all 4 aces?
Again, you are dealt 4 cards. The first card is a spade, the second a heart, the third a diamond, and the fourth a club. What is the probability that you are dealt all 4 aces?
Again, consider the roll of a 6-sided die. Given the following events A and B, find the intersection and the union for A and B if (a) A = {1,3, 5] and B = {2,4,6} (b) A = {1,3} and B = {1,3,5} (c) A=
Consider the roll of a 6-sided die, its faces numbered 1, 2, 3, 4, 5, and 6. Draw a Venn diagram showing the six possible outcomes. Now draw circles showing the following rolls:(a) An odd number(b) 2
You have drawn three diamonds, one spade, and one heart from a deck of cards.If you discard the spade and the heart, what is the probability of your drawing two cards from the remaining 47 cards to
In poker, a royal flush consists of A, K, Q, J, and ten of the same suit. What is the probability of drawing five cards and obtaining a royal flush? What is the probability of being dealt a royal
Suppose there are six unrelated people in a room. What is the probability that any two of them have the same birthday?
Suppose you toss a coin three times. What is the probability of tossing three heads in a row? What is the probability of tossing three tails in a row? What is the probability of tossing either three
An advertising executive decides that a television commercial should be shown on two television stations. If three television stations serve the area the company wants to reach, how many possible
An automobile manufacturer produces cars in four different colors and offers three different options packages. How many different combinations of color and options package can the auto manufacturer
A basketball player makes 75 % of his shots from the foul line. What is the probability of this player making 10 shots in a row from the foul line? Are there any assumptions we need to make to
Your investment advisor has a portfolio of 75 stocks: 40 high-growth stocks and 35 high-dividend stocks. Of the 40 high-growth stocks, 25 have increased in value over the last year, whereas 10 of the
The Whiter Smile Company is about to begin selling a new toothpaste. Company planners know that the probability of the new product being profitable is 10 %. They also know from previous market
Suppose you flip a fair coin once and roll a 6-sided die once. What is the probability of tossing a tail and rolling a one?
Suppose you flip a coin twice and roil a die twice. What is the probability that you will toss 1 head and 1 tail and will roll two 6’s?
A top amateur bowler has a 70 % chance of roiling a strike. What is the probability that this bowler will bowl a perfect game (12 strikes in a row)?Are there any assumptions we need to make to answer
The Tastee Coffee Company is about to begin selling a new gourmet coffee.Company managers know that the probability the product will be profitable is 20 %. They also know that the probability that
A real estate developer offers homes in five different colors and three different models. How many different combinations of color and model can the real estate developer offer?
Rah Rah College has a limited number of dorm rooms available to students, so every year students participate in a lottery to determine whether they will have school housing next year. Suppose that
A stock broker owns five suits and 12 ties. Assuming that all the suits and ties match, determine how many different outfits (combinations) the stock broker can wear.
An advertising agency suggests that a bicycle manufacturer advertises in four of the seven bicycling magazines. How many different combinations of four magazines can be selected?
A Senate committee consists of six Democrats and five Republicans. In how many ways can a subcommittee consisting of four Democrats and four Republicans be formed?
You believe you have come up with a fool-proof way to win at roulette.Because the odds are nearly 50–50 that red will come up and nearly 50–50 that black will come up in roulette, you believe
At the beginning of each week, a company decides how much to spend on newspaper ads for that week. It spends either $250 or $500 each week on newspaper ads. Assuming there is an equal probability of
A car salesman meets 12 customers each week. His probability of making a sale in the first meeting with a customer is .3. When he gets the second meeting with the same customer, the probability of
A life insurance company knows with certainty that all people will die someday.Does it make sense for the insurance company to use probability theory to set its life insurance rates?
Consider the sample space S = {A, B, C, D, E, F, G} and the following events:Are the following sets of events mutually exclusive, collectively exhaustive, both, or neither? I = {A, C, E, G} II = {B,
State the complement of each of the following events:(a) Drawing a spade from a full deck of cards(b) Inflation of less than 5 % per year(c) GNP growth of more than 4 % per year
The figure below is a plot of salary and experience of employees of the Endicott Company. Answer the following questions by using a Venn diagram.(a) The probability of experience between 3 and 5
All the students of a university are assigned ID numbers. The ID number consists of the first three letters of a student’s last name, followed by four numbers. How many possible different ID
Suppose there are four events A, B, C, and D. The following information is given: P(A) = .5 P(B) = .15 P(C) = .20 P(AUD) = .72 P(A | B) = .25 P(AC) = .04 P(AD) = .03
Assume you have applied to two different universities A and B. In the past, 30 % of students who applied to University A were accepted, while University B accepted 45 % of the applicants. Assume
Suppose 20 % of the employees of company ABC have only a high school diploma, 60 % have bachelor degrees, and 20 % have graduate degrees Of those with only a high school diploma, 15 % hold management
A sports magazine wants to learn something about its subscribers. The subscribers are classified as teenagers or older people and as being in school or holding a job. The magazine sends out a
The following picture helps you obtain the probability that events A, B, and C, happen jointly. Write down the formula for obtaining P(ANBNC).
A hospital found that the probability of a power failure in a certain time period is .00001. To guarantee the functioning of the hospital, the hospital installed a backup system that has a
Predict the monthly sales for next month if $400 is spent on advertising. Use a 95% prediction interval.
Refer to the sales-appraisal simple linear regression in previous examples. Find a 95% confidence interval for the mean monthly sales when the appliance store spends $400 on advertising.Previous
Calculate the coefficient of determination for the advertising-sales example.Obtaining the Value of The data are repeated in Table 11.4 for convenience. Interpret the result. Table 11.4
Legalized gambling is available on several riverboat casinos operated by a city in Mississippi. The mayor of the city wants to know the correlation between the number of casino employees and the
Refer to the simple linear regression analysis of the advertising-sales data, Examples 11.2 and 11.3. Conduct a test (at α = .05) to determine if sales revenue (y) is linearly related to advertising
Refer to the advertising–monthly sales data presented in Table 11.1. Consider the straight-line model, E(y) = β0 + β1x, where y = sales revenue (thousands of dollars) and x = advertising
Consider a study designed to estimate the linear relationship between the percentage of jobs outsourced to another country by a U.S. company and the size (number of employees) of the company. In
A large firm has established what it hopes is an objective system of deciding on annual pay increases for its employees. The system is based on a series of evaluation scores determined by the
Refer to Example 9.10. Suppose the same factorial experiment is performed on four other brands (E, F, G, and H), and the results are as shown in Table 9.16. Repeat the factorial analysis and
The USGA is interested in knowing whether the difference in distance traveled by any two golf ball brands depends on the club used. Consequently, the USGA tests four different brands (A, B, C, D) of

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