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statistics

Elementary Statistics 3rd Canadian Edition Mario F. Triola - Solutions

The probability that a person owns an imported vehicle is 0.43. The probability that a vehicle is more than 5 years old is 0.28. The probability that a vehicle is an import over 5 years old is 0.09. a. Create a contingency table based on these probabilities. b. What is the probability that a
Remote sensors are used to control each of two separate and independent valves, denoted by p and q, which must both open to provide water for emergency cooling of a nuclear reactor. Each valve has a 0.95 probability of opening when triggered. For the given configuration, find the probability that
The probability that a household has an annual income of under $100,000 is 0.72. The probability that a household donates less than $200 per year to charity is 0.63. The probability that a household has an annual income of at least $100,000 and donates at least $200 per year to charity is 0.15. a.
The probability that a person does his or her own return is 0.85. The probability that a person receives a refund is 0.76. The probability that a person does his or her own return and receives a refund is 0.68. a. Create a contingency table based on these probabilities. b. Who is more likely to
When driving to class, a student must pass 2 traffic lights that operate independently. For each light, there is a 0.4 probability that it is green. If she must reach both lights when they are green in order to make class on time, what is the probability that she will be on time?
The probability that a student receives an A in a course is 0.1. The probability that a student studies less than 30 hours per week is 0.503. The probability that a student studies less than 30 hours per week and receives less than an A in a course is 0.495. a. Create a contingency table based on
The probability that a person exercises regularly is 0.212. The probability that a person lives to the age of 80 or more is 0.30694. The probability that a person does not exercise regularly and lives to the age of 80 or more is 0.159176. a. Create a contingency table based on these
Using funding from Ontario's "Super build" Program, a contractor bought a box of decorative screws. Five of the screws are slotted, four are designed for a Phillips-head screwdriver, and three are designed for a square-tipped screwdriver. If two of the screws are randomly selected from the box,
Seven financial experts participated in a stock market selection game. Their first choice had to be selected from 8 different resource stocks. All 7 experts picked the same resource stock. If the picks were purely at random, what is the probability of this event occurring?
As an insurance claims investigator, you are suspicious of 4 brothers who each reported a stolen car in a different region of Montreal. If Montreal has an annual car-theft rate of 4.5%, find the probability that among 4 randomly selected cars, all are stolen in a given year. What does the result
A blood-testing procedure is made more efficient by combining samples of blood specimens. If samples from 5 people are combined, the mixture will test positive except if all 5 individual samples are negative. Find the probability of a positive result for 5 samples combined into 1 mixture, assuming
An employee claims that a new process for manufacturing DVD players is better because the rate of defects is below 5%, the rate of defects in the past. When 20 DVD players are manufactured with the new process, there are no defects. Assuming that the new method has the same 5% defect rate as in the
The probability that a household has an annual income of $80,000 or more is 0.26. The probability that a household owns an SUV, given that it has an annual income of $80,000 or more is 0.42. The probability that a household owns an SUV, given that it has an annual income under $80,000 is 0.36. a.
The market share of three furniture manufacturers is 21.7% for A, 34.6% for B, and 43.7% for C. The percentage of each manufacturer's production that is sold to high-end furniture stores is 89.4%, 60.3%, and 40.7%, respectively for A, B, and C. a. What is the overall percentage of the companies'
In a survey of those aged 18 or older, 18% of the respondents are aged 18-24, 29% are aged 25-44, and 38% are aged 45-64. The percentage of the respondents in each age group who own their home is 0.2%, 25.4%, 63.2%, and 83.7% for those aged 18-24, 25-44, 45-64, and 65 or older, respectively. a.
Of those with a university degree, 70.2% earn at least $60,000 per year within 10 years of finishing school. Of those without a university degree, the corresponding percentage is 35.4%. Of the entire population, 24.6% have a university degree. a. What percentage of the entire population earns at
Find the probability that of 25 randomly selected people, a. No 2 share the same birthday. b. At least 2 share the same birthday.
Two cards are to be randomly selected without replacement from a shuffled deck. Find the probability of getting a 10 on the first card and a club on the second card.
Find the probability of answering the first 2 questions on a test correctly if random guesses are made and a. The first 2 questions are both true/false types. b. The first 2 questions are both multiple choice, each with 5 possible answers.
A recycling firm collected recycling statistics for three cities, A, B, and C. The percentage of the total number of residents in each city is 45% in A, 30% in B, and 25% in C. The percentage in each city that recycles is 12% in A, 18% in B, and 30% in C. Of those that recycle, the percentage that
Find the probability of getting 4 consecutive aces when 4 cards are drawn without replacement from a shuffled deck.
We have noted that when rolling a pair of dice, there are 36 different possible outcomes: 1-1, 1-2, . . . , 6-6. a. What is the probability of rolling a 7? b. If you have just entered a friendly neighbourhood game of craps and the person who brought the dice rolls eight consecutive 7s, what do you
A classic excuse for a missed test is offered by 4 students who claim that their car had a flat tire. On the makeup test, the instructor asks the students to identify the particular tire that went flat. If they didn't really have a flat tire and randomly select one that supposedly went flat, what
Three firms using the same auditor independently and randomly select a month in which to conduct their annual audits. What is the probability that all 3 months are different?
In a market survey of Zellers, a researcher is told that 76% of customers are repeat customers. If 10 customers are selected at random, what is the probability that all 10 are repeat customers? Would this be a very common occurrence?
Ignoring leap years, find the probability that 3 randomly selected people were all born on September 24.
A Statistics Canada study of environmental impacts on human health in 5 provinces indicates that a male has a 0.133 chance of dying in any type of accident. Find the probability that 5 randomly selected males will all eventually die in an accident.
Evaluate the given expressions. 40C6
Evaluate the given expressions. 40P6
Evaluate the given expressions. nC0
Evaluate the given expressions. nP0
Evaluate the given expressions. nPn
Evaluate the given expressions. nCn
The author uses a home security system that has a code consisting of 4 digits (0, 1, . . . , 9) that must be entered in the correct sequence. The digits can be repeated in the code. a. How many different possibilities are there? b. If it takes a burglar 5 seconds to try a code, how long would it
There are 12 members on the board of directors for Cliffside General Hospital. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of 4 members, how
Each social insurance number (SIN) is a sequence of 9 digits. What is the probability of randomly generating 9 digits and getting your SIN number?
In doing a runs test for randomness (Section 12-7), it is found that genders of survey subjects listed in consecutive order are as follows: MMMMMMM-MMMFFFFFFFF. How many different ways can those letters be arranged?
A Federal Express delivery route must include stops at 5 cities. a. How many different routes are possible? b. If the route is randomly selected, what is the probability that the cities will be arranged in alphabetical order?
a. If a couple plans to have 8 children (it happens), how many different gender sequences are possible? b. If a couple has 4 boys and 4 girls, how many different gender sequences are possible? c. Based on the results from .parts (a) and (b), what is the probability that when a couple has 8
Suppose you bought a ticket in a lottery that requires you to select 6 distinct numbers between 1 and 40 inclusive. a. How many different selections are possible? b. What is the probability of winning with one ticket? c. What are the odds against winning such a lottery with one ticket?
Refer to the same lottery described in Exercise 25. What is the probability of winning if the rules are changed so that you must select the correct 6 numbers in the same order in which they are drawn?
In Denys Parsons' Directory of Tunes and Musical Themes, melodies for more than 14,000 songs are listed according to the following scheme: The first note of every song is represented by an asterisk (*), and successive notes are represented by R (for repeat the previous note), 17 (for a note that
M.S. and Associates would like to design a mutual fund portfolio from 50 eligible Canadian equity funds. The portfolio must be made up of 4 funds. a. How many different portfolios are possible? b. If the funds are selected at random (which we hope they are not), what is the probability of getting
Evaluate the given expressions. 100!/97!
You become suspicious when a genetics researcher randomly selects groups of 20 newborn babies and seems to consistently get 10 girls and 10 boys. The researcher explains that it is common to get 10 boys and 10 girls in such cases. a. If 20 newborn babies are randomly selected, how many different
The Halifax Music Company has purchased the rights to 15 different songs and it plans to release a new CD with 8 of them. Recognizing that the order of the songs is important, how many different CDs are possible?
a. How many different postal codes are possible if each code is two sequences, the first sequence being letter-number-letter (for example, El A) and the second sequence being number-letter-number (for example, 3E9)? b. If a computer randomly generates postal codes, what is the probability that it
Because of recent retirements, 8 management positions became open at the Red River Finance Company. The jobs were all at different levels of management. A total of 22 employees applied for these management positions. How many different ways could the company fill the 8 vacancies?
In an age-discrimination case against Darmin, Inc., evidence showed that among the last 40 applicants for employment, only the 8 youngest were hired. Find the probability of randomly selecting 8 of 40 people and getting the 8 youngest. Based on the result, does it appear that age discrimination is
The following excerpt is from The Man Who Cast Two Shadows, by Carol O'Connell: "The child had only the numbers written on her palm in ink . . . all but the last four numbers disappeared in a wet smudge of blood. . . . She would put the coins into the public telephones and dial three untried
After testing 12 homes for the presence of radon, an inspector is concerned that her test equipment is defective because the measured radon level at each home was higher than the reading at the preceding home. That is, the 12 readings were arranged in order from low to high. If the homes were
A freight train is to carry 12 coal cars, 5 cars full of lumber, and 4 tankers all carrying kerosene. How many different arrangements are possible?
How many 6-digit license plates are possible? How many plates are possible if no digits can be repeated? How many plates are possible if 1 letter replaces one of the 6 digits (no repeated digits)?
Evaluate the given expressions. 85!/82!
Once upon a time, a common computer programming rule was that names of variables must be between 1 and 8 characters long. The first character could be any of the 26 letters, while successive characters could be any of the 26 letters or any of the 10 digits. For example, allowable variable names
a. Five managers gather for a meeting. If each manager shakes hands with each other manager exactly once, what is the total number of handshakes? b. If n managers shake hands with each other exactly once, what is the total number of handshakes? c. How many different ways can 5 managers be seated at
Many calculators or computers cannot directly calculate 70! or higher. When n is large, n\ can be approximated by n\ = 10K where K = (n + 0.5) log n + 0.39908993 - 0.43429448«. a. Evaluate 50! using the factorial key on a calculator and also by using the approximation given here. b. Canada Post
Can computers "think"? According to the Turing test, a computer can be considered to think if, when a person communicates with it, the person believes he or she is communicating with another person instead of a computer. In an experiment at Boston's Computer Museum, each of 10 judges communicated
Evaluate the given expressions. 12P9
If one of the 500 car owners is randomly selected, find the probability of getting a foreign car owner.
On the basis of past experience, a commuting student knows that when he speeds on any given day, there is a 2% chance of being ticketed. What is the probability of not getting a speeding ticket if he speeds every one of the 150 days in one year of college? If this student cannot afford the
The board of directors for the Southern Alberta Insurance Company has 8 members. a. If a committee of 3 is formed by random selection, what is the probability that it consists of the 3 wealthiest members? b. If the board must elect a chairperson, vice chairperson, and secretary, how many different
You choose 5 Canadian equity mutual funds for your portfolio. The probability that each fund will rise in value next year is 87.5%. What is the probability that all 5 funds will rise in value next year?
When betting on even in roulette, there are 38 equally likely outcomes, but only 2, 4, 6, . . . , 36 are winning outcomes. a. Find the probability of winning when betting on even. b. Find the odds against winning with a bet on even. c. Casinos pay winning bets according to odds described as 1:1.
A question on a history test requires that 5 events be arranged in the proper chronological order. If a random arrangement is selected, what is the probability that it will be correct?
A pollster claims that 12 voters were randomly selected from a population of 200,000 voters (30% of whom are Progressive Conservatives), and all 12 were Progressive Conservatives. The pollster claims that this could easily happen by chance. Find the probability of getting 12 Progressive
In a statistics class of 8 women and 8 men, 2 groups of 8 students are formed by random selection. What is the probability that all of the women are in the first group and all of the men are in the second group?
If one of the 500 car owners is randomly selected, find the probability of getting a foreign car owner or someone who lives in a large city.
If two different car owners are randomly selected, find the probability that both people live in a rural area.
If one owner is randomly selected, find the probability of getting someone who lives in the suburbs or in a rural area.
If three different owners are randomly selected, find the probability that they all own domestic cars.
If one car owner is randomly selected, find the probability of getting someone who lives in a large city, given that her or his car is foreign. Are owning a foreign car and living in large cities independent events? Why or why not?
In a census of households, 25% own a high-definition TV, 17% own a camcorder, and 6.2% own both devices. If a household is randomly selected, what is the probability that it owns either device?
Refer to the accompanying frequency table, which describes the age distribution of Canadians who died of cancer (based on data from Statistics Canada).a. Assuming that the class of "75 and over" has a class midpoint of 80, calculate the mean age of the Canadians who died of cancer.b. Using the same
The accompanying box plot depicts heights (in inches) of a large collection of randomly selected adult women.a. If one of these women is randomly selected, find the probability that her height is between 56.1 in. and 62.2 in.b. If one of these women is randomly selected, find the probability that
A zookeeper is interested in the lengths of pregnancies of mammals. The gestation periods (in days) of 12 randomly selected mammal species are listed below. 260 42 16 350 280 230 337 113 68 44 13 62 a. Find the mean gestation period for the sample. b. Find the median gestation
A manufacturing process is continually monitored for defective parts. Every hour 5 samples are taken from the process. Listed here are the number of defective parts in a sample of 5 and the probability associated with each.Determine whether a probability distribution is given. In those cases where
A study of gender bias in television news involves the selection of guests and reporters on CBC's The National. The people appearing on air during a certain period are randomly selected in groups of 4 and the numbers of women are recorded. The probabilities of getting 0, 1, 2, 3, and 4 women are
When you give a casino $5 for a bet on the number 7 in roulette, you have a 1/38 probability of winning $175 and a 37/38 probability of losing $5. What is your expected value? In the long run, how much do you lose for each dollar bet?
Based on past results found in the Information Please Almanac, there is a 0.120 probability that a baseball World Series contest will last four games, a 0.253 probability that it will last five games, a 0.217 probability that it will last six games, and a 0.410 probability that it will last seven
If the probability of being killed by lightning is 0.000002 for a one-year period, what is the expected value of a one-year insurance policy that would pay $1 million if you are killed by lightning?
Reader's Digest recently ran a sweepstakes in which prizes were listed along with the chances of winning: $5,000,000 (1 chance in 201,000,000), $150,000 (1 chance in 201,000,000), $100,000 (1 chance in 201,000,000), $25,000 (1 chance in 100,500,000), $10,000 (1 chance in 50,250,000), $5000 (1
The random variable x represents the number of girls in a family of 3 children. Find the mean, variance, and standard deviation for the random variable x. Also, use the range rule of thumb (from Section 2-5) to approximate the minimum and maximum usual values of x.
The random variable x represents the number of boys in a family of 4 children. (See Exercise 17.) Find the mean, variance, and standard deviation for the random variable x. Also, use the range rule of thumb (from Section 2-5) to approximate the usual minimum and maximum values of x.
The Don Mills Electronics Company makes switching devices for traffic signals. One batch of 10 switches includes 2 that are defective. If 2 switches are randomly selected from that batch without replacement, let the random variable x represent the number that are defective. Find the mean, variance,
The cost of a randomly selected textbook
A statistics class includes 3 left-handed students and 24 right-handed students. Two different students are randomly selected for a data collection project and the random variable x represents the number of left-handed students selected. Find the mean, variance, and standard deviation for the
In each case, determine whether the given function is a probability distribution. a. P(x) = 1/2x where x = 1, 2, 3,... b. P(x) = 1/2x where x = 1, 2, 3,... c. P(x) = 3/ [4(3 - x)!x!] where x = 0,1,2, 3 d. P(x) = 0.4(0.6)x-1 where x = 1, 2, 3,...
The mean and standard deviation for a random variable x are 5.0 and 2.0, respectively. Find the mean and standard deviation if a. each value of x is increased by 3 b. each value of x is multiplied times 3 c. each value of x is multiplied times 3 and then 4 is added
Digits (0, 1, 2,. . . ,9) are randomly selected for telephone numbers in surveys. The random variable x is the selected digit. a. Find the mean and standard deviation of x.b. Find the z score for each of the possible values of x, then find the mean and standard deviation of the population of z
Assume that the discrete random variable x can assume the values 1, 2,..., n, and that those values are equally likely.a. Show that µ. = (n + l)/2.b. Show that σ2 = (n2 - 1)/12.c. An experiment consists of randomly selecting a whole number between 1 and 50, and the random variable x is the value
Let the random variable x represent the number of girls in a family of four children. Construct a table describing the probability distribution, then find the mean and standard deviation. (Hint: Begin by listing the different possible outcomes.)
The amount of milk obtained from a cow
When a household is randomly selected, the probability distribution for the number x of automobiles owned is as described in the accompanying table.Determine whether a probability distribution is given. In those cases where a probability distribution is not described, identify the requirement that
If your college hires the next 4 employees without regard to gender, and the pool of applicants is large with an equal number of men and women, then the probability distribution for the number x of women hired is described in the accompanying table.Determine whether a probability distribution is
In assessing credit risks, a bank investigates the number of credit cards people have. With x representing the number of credit cards adults have, the accompanying table describes the probability distribution for a population of applicants (based on data from Maritz Marketing Research,
The Willford Printing Company conducted a survey to monitor daily absenteeism at the plant. The accompanying table describes the probability distribution for one department at the plant, where x represents the number of employees absent in the department.Determine whether a probability distribution
Assume that in a procedure that yields a binomial distribution, a trial is repeated n times. Find the probability of x successes given the probability p of success on a single trial. Use the given values of n, x, and p and the binomial probability formula or statistical software. n = 3, x = 2, p =
Assume that in a procedure that yields a binomial distribution, a trial is repeated n times. Find the probability of x successes given the probability p of success on a single trial. Use the given values of n, x, and p and the binomial probability formula or statistical software. n = 6, x = 2, p =
Assume that in a procedure that yields a binomial distribution, a trial is repeated n times. Find the probability of x successes given the probability p of success on a single trial. Use the given values of n, x, and p and the binomial probability formula or statistical software. n = 10, x = 4, p =

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