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theory of statistics

Questions and Answers of Theory of Statistics

In a binomial distribution n = 12 and π = .60. Find the following probabilities.a. x = 5.b. x ≤ 5.c. x ≥ 6.
In a binomial distribution n = 8 and π = .30. Find the probabilities of the following events.a. x = 2.b. x ≤ 2 (the probability that x is equal to or less than 2).c. x ≥ 3 (the probability that
For a case where n = 4 and π = .60, determine the probability that:(a) x = 2.(b) x ≤ 2.(c) x > 2.
A study by the Illinois Department of Transportation concluded that 76.2 percent of front seat occupants used seat belts. That means that both occupants of the front seat were using their seat belts.
Can you tell the difference between Coke and Pepsi in a blind taste test?Most people say they can and have a preference for one brand or the other.However, research suggests that people can correctly
A recent survey by the American Accounting Association revealed 23 percent of students graduating with a major in accounting select public accounting. Suppose we select a sample of 15 recent
A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find:a. The probability of making exactly four sales.b. The
Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday.a. What is the probability
The United States Postal Service reports 95 percent of first class mail within the same city is delivered within two days of the time of mailing. Six letters are randomly sent to different
An American Society of Investors survey found 30 percent of individual investors use a discount broker. In a random sample of nine individuals, what is the probability:a. Exactly two of the sampled
Assume a binomial distribution where n = 5 and π = .30.a. Refer to Appendix B.7 and list the probabilities for values of x from 0 to 5.b. Determine the mean and standard deviation of the
Assume a binomial distribution where n = 3 and π = .60.a. Refer to Appendix B.7 and list the probabilities for values of x from 0 to 3.b. Determine the mean and standard deviation of the
In a binomial situation n = 5 and π = .40. Determine the probabilities of the following events using the binomial formula.a. x = 1b. x = 2
In a binomial situation n = 4 and π = .25. Determine the probabilities of the following events using the binomial formula.a. x = 2b. x = 3
Five percent of the worm gears produced by an automatic, highspeed Carter-Bell milling machine are defective. What is the probability that out of six gears selected at random none will be defective?
There are five flights daily from Pittsburgh via US Airways into the Bradford, Pennsylvania, Regional Airport. Suppose the probability that any flight arrives late is .20. What is the probability
The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 250 customers on the number of hours cars are parked and the amount they are charged.a. Convert
Belk Department Store is having a special sale this weekend. Customers charging purchases of more than $50 to their Belk credit card will be given a special Belk Lottery card. The customer will
The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. What is the expected number of
The information below is the number of daily emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina, for the last 50 days. To explain, there were 22 days on
Which of these variables are discrete and which are continuous random variables?a. The number of new accounts established by a salesperson in a year.b. The time between customer arrivals to a bank
Three tables listed at the top of the next page show “random variables”and their “probabilities.” However, only one of these is actually a probability distribution.a. Which is it?b. Using the
Compute the mean and variance of the following discrete probability distribution. x 280 10 P(x) 532
Compute the mean and variance of the following discrete probability distribution. 123 x 0 P(x) .2 431 .3
The Pizza Palace offers three sizes of cola—small, medium, and large—to go with its pizza. The colas are sold for $0.80, $0.90, and $1.20, respectively. Thirty percent of the orders are for
John Ragsdale sells new cars for Pelican Ford. John usually sells the largest number of cars on Saturday. He has developed the following probability distribution for the number of cars he expects to
The possible outcomes of an experiment involving the roll of a six-sided die are a one-spot, a two-spot, a three-spot, a four-spot, a five-spot, and a sixspot.(a) Develop a probability distribution
Suppose we are interested in the number of heads showing face up on three tosses of a coin. This is the experiment. The possible results are:zero heads, one head, two heads, and three heads. What is
Describe the characteristics of and compute probabilities using the Poisson probability distribution.
Describe the characteristics of and compute probabilities using the binomial probability distribution.
Distinguish between discrete and continuous probability distributions.
Define the terms probability distribution and random variable.
Refer to the Wages data, which report information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of education, and gender for each worker.
Refer to the Baseball 2006 data, which reports information on the 30 Major League Baseball teams for the 2006 season. Set up a variable that divides the teams into two groups, those that had a
Refer to the Real Estate data, which reports information on homes sold in the Denver, Colorado, area during the last year.a. Sort the data into a table that shows the number of homes that have a pool
During the 1970s the game show Let’s Make a Deal had a long run on TV. In the show a contestant was given a choice of three doors, behind one of which was a prize. The other two doors contained a
Two components, A and B, are in series. (Being in series means that for the system to operate, both components A and B must work.) Assume the two components are independent. What is the probability
A puzzle in the newspaper presents a matching problem. The names of 10 U.S. presidents are listed in one column, and their vice presidents are listed in random order in the second column. The puzzle
A case of 24 cans contains 1 can that is contaminated. Three cans are to be chosen randomly for testing.a. How many different combinations of 3 cans could be selected?b. What is the probability that
A computer password consists of four characters. The characters can be one of the 26 letters of the alphabet. Each character may be used more than once. How many different passwords are possible?
Tim Bleckie is the owner of Bleckie Investment and Real Estate Company. The company recently purchased four tracts of land in Holly Farms Estates and six tracts in Newburg Woods. The tracts are all
There are four people being considered for the position of chief executive officer of Dalton Enterprises. Three of the applicants are over 60 years of age. Two are female, of which only one is over
The state of Maryland has license plates with three numbers followed by three letters. How many different license plates are possible
A new sports car model has defective brakes 15 percent of the time and a defective steering mechanism 5 percent of the time. Let’s assume (and hope) that these problems occur independently. If one
Reynolds Construction Company has agreed not to erect all “look-alike”homes in a new subdivision. Five exterior designs are offered to potential home buyers. The builder has standardized three
A new chewing gum has been developed that is helpful to those who want to stop smoking. If 60 percent of those people chewing the gum are successful in stopping smoking, what is the probability that
It was found that 60 percent of the tourists to China visited the Forbidden City, the Temple of Heaven, the Great Wall, and other historical sites in or near Beijing. Forty percent visited Xi’an
Several years ago Wendy’s Hamburgers advertised that there are 256 different ways to order your hamburger. You may choose to have, or omit, any combination of the following on your hamburger:
For the daily lottery game in Illinois, participants select three numbers between 0 and 9. A number cannot be selected more than once, so a winning ticket could be, say, 307 but not 337. Purchasing
With each purchase of a large pizza at Tony’s Pizza, the customer receives a coupon that can be scratched to see if a prize will be awarded.The odds of winning a free soft drink are 1 in 10, and
An investor purchased 100 shares of Fifth Third Bank stock and 100 shares of Santee Electric Cooperative stock. The probability the bank stock will appreciate over a year is .70. The probability the
A computer-supply retailer purchased a batch of 1,000 CD-R disks and attempted to format them for a particular application. There were 857 perfect CDs, 112 CDs were usable but had bad sectors, and
An Internet company located in Southern California has season tickets to the Los Angeles Lakers basketball games. The company president always invites one of the four vice presidents to attend games
Althoff and Roll, an investment firm in Augusta, Georgia, advertises extensively in the Augusta Morning Gazette, the newspaper serving the region. The Gazette marketing staff estimates that 60
A recent survey reported in BusinessWeek dealt with the salaries of CEOs at large corporations and whether company shareholders made money or lost money.If a company is randomly selected from the
The board of directors of Saner Automatic Door Company consists of 12 members, 3 of whom are women. A new policy and procedures manual is to be written for the company. A committee of 3 is randomly
There are 20 families living in the Willbrook Farms Development. Of these families 10 prepared their own federal income taxes for last year, 7 had their taxes prepared by a local professional, and
Refer to Exercise 56, but assume there are 10 homes in the Quail Creek area and four of them have a security system. Three homes are selected at random:a. What is the probability all three of the
Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random:a. What is the probability all three of the selected homes have a security
Brooks Insurance, Inc., wishes to offer life insurance to men age 60 via the Internet. Mortality tables indicate the likelihood of a 60-year-old man surviving another year is .98. If the policy is
Ninety students will graduate from Lima Shawnee High School this spring. Of the 90 students, 50 are planning to attend college. Two students are to be picked at random to carry flags at the
The probability that a cruise missile hits its target on any particular mission is .80. Four cruise missiles are sent after the same target. What is the probability:a. They all hit the target?b. None
Joe Mauer of the Minnesota Twins had the highest batting average in the 2006 Major League Baseball season. His average was .347. So assume the probability of getting a hit is .347 for each time he
There are 100 employees at Kiddie Carts International. Fifty-seven of the employees are production workers, 40 are supervisors, 2 are secretaries, and the remaining employee is the president. Suppose
Assume the likelihood that any flight on Northwest Airlines arrives within 15 minutes of the scheduled time is .90. We select four flights from yesterday for study.a. What is the likelihood all four
In a management trainee program at Claremont Enterprises, 80 percent of the trainees are female and 20 percent male. Ninety percent of the females attended college, and 78 percent of the males
Armco, a manufacturer of traffic light systems, found that under accelerated-life tests, 95 percent of the newly developed systems lasted 3 years before failing to change signals properly.a. If a
The first card selected from a standard 52-card deck is a king.a. If it is returned to the deck, what is the probability that a king will be drawn on the second selection?b. If the king is not
Berdine’s Chicken Factory has several stores in the Hilton Head, South Carolina, area. When interviewing applicants for server positions, the owner would like to include information on the amount
The probability that the cause and the cure for all cancers will be discovered before the year 2010 is .20. What viewpoint of probability does this statement illustrate?
The number of times a particular event occurred in the past is divided by the number of occurrences. What is this approach to probability called
The marketing research department at Vernors plans to survey teenagers about a newly developed soft drink. Each will be asked to compare it with his or her favorite soft drink.a. What is the
A company is creating three new divisions and seven managers are eligible to be appointed head of a division. How many different ways could the three new heads be appointed?
USA Today/Gallup Polls developed 15 questions designed to rate the performance of the president of the United States. They will select 10 of these questions. How many different arrangements are there
A representative of the Environmental Protection Agency (EPA) wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples
An overnight express company must include five cities on its route. How many different routes are possible, assuming that it does not matter in which order the cities are included in the routing?
A telephone number consists of seven digits, the first three representing the exchange. How many different telephone numbers are possible within the 537 exchange?
There are 10 members on the Community Appearance Board of Los Angeles County. This board is charged with ensuring that all new construction projects meet county appearance standards. A new terminal
In a lottery game, three numbers are randomly selected from a tumbler of balls numbered 1 through 50.(a) How many permutations are possible?(b) How many combinations are possible?
In the above example involving Goody Records, we said that eight colors taken three at a time would give 56 different combinations.(a) Use formula (5–9) to show this is true.(b) As an alternative
The 10 numbers 0 through 9 are to be used in code groups of four to identify an item of clothing. Code 1083 might identify a blue blouse, size medium; the code group 2031 might identify a pair of
A machine operator must make four safety checks before machining a part. It does not matter in which order the checks are made. In how many different ways can the operator make the checks?
A musician wants to write a score based on only five chords: B-flat, C, D, E, and G. However, only three chords out of the five will be used in succession, such as C, B-flat, and E. Repetitions, such
The marketing department has been given the assignment of designing color codes for the 42 different lines of compact disks sold by Goody Records. Three colors are to be used on each CD, but a
Betts Machine Shop, Inc., has eight screw machines but only three spaces available in the production area for the machines. In how many different ways can the eight machines be arranged in the three
Referring to the group of three electronic parts that are to be assembled in any order, in how many different ways can they be assembled?
(a) The Women’s Shopping Network on cable TV offers sweaters and slacks for women. The sweaters and slacks are offered in coordinating colors. If sweaters are available in five colors and the
An automobile dealer wants to advertise that for $29,999 you can buy a convertible, a two-door sedan, or a four-door model with your choice of either wire wheel covers or solid wheel covers. How many
If you ask three strangers about their birthdays, what is the probability:(a) All were born on Wednesday? (b) All were born on different days of the week? (c) None were born on Saturday?
The board of directors of a small company consists of five people. Three of those are “strong leaders.” If they buy an idea, the entire board will agree. The other “weak” members have no
An investor owns three common stocks. Each stock, independent of the others, has equally likely chances of (1) increasing in value, (2)decreasing in value, or (3) remaining the same value. List the
Each salesperson at Puchett, Sheets, and Hogan Insurance Agency is rated either below average, average, or above average with respect to sales ability. Each salesperson is also rated with respect to
Three defective electric toothbrushes were accidentally shipped to a drugstore by Cleanbrush Products along with 17 nondefective ones.a. What is the probability the first two electric toothbrushes
Refer to the following table.a. Determine P(A1).b. Determine P(B1|A2).c. Determine P(B2 and A3). A Total First Event 1 3 213 2113 Second Event B A, B Total 640 4 10
All Seasons Plumbing has two service trucks that frequently break down.If the probability the first truck is available is .75, the probability the second truck is available is .50, and the
A local bank reports that 80 percent of its customers maintain a checking account, 60 percent have a savings account, and 50 percent have both. If a customer is chosen at random, what is the
Suppose and and P(X1) = .75 and P(Y2 | X1) = .40. What is the joint probability of X1 and Y2?
Suppose P(A) = .40 and P(B|A) = .30. What is the joint probability of A and B?
Consumers were surveyed on the relative number of visits to a Circuit City store (often, occasional, and never) and if the store was located in an enclosed mall (yes and no). When variables are
Refer to Table 5–1.(a) What is the probability of selecting an executive with more than 10 years of service?(b) What is the probability of selecting an executive who would not remain with the

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