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statistics
elementary statistics a step by step approach
Elementary Statistics A Step By Step Approach 9th Edition Allan G. Bluman - Solutions
For a banquet, a committee can select beef, pork, chicken, or veal; baked potatoes or mashed potatoes; and peas or green beans for a vegetable. Draw a tree diagram for all possible choices of a meat, a potato, and a vegetable.
At a sorority meeting, there are 6 seniors, 4 juniors, and 2 phomores. If a committee of 3 is to be formed, find the probability that 1 of each will be selected.
A coin is tossed 5 times; find the probability of getting at least 1 tail. Would you consider this event likely to happen? Explain your answer.
A cruise director schedules 4 different movies, 2 bridge games, and 3 tennis games for a two-day period. If a couple selects 3 activities, find the probability that they attend 2 movies and 1 tennis game.
On a lunch counter, there are 3 oranges, 5 apples, and 2 bananas. If 3 pieces of fruit are selected, find the probability that 1 orange, 1 apple, and 1 banana are selected.
How many different ways can 5 cellular telephones be selected from 8 cellular phones?
A physics test consists of 25 true/false questions. How many different possible answer keys can be made?
If 4 cards are drawn from a deck of 52 and not replaced, find the probability of getting at least 1 club.
How many different arrangements of the letters in the word number can be made?
One company’s ID cards consist of 5 letters followed by 2 digits. How many cards can be made if repetitions are allowed? If repetitions are not allowed?
A soda machine servicer must restock and collect money from 15 machines, each one at a different location. How many ways can she select 4 machines to service in 1 day?
How many different ways can 8 speakers be seated on a stage?
If a student can select 5 novels from a reading list of 20 for a course in literature, how many different possible ways can this selection be done?
How many ways can 5 sopranos and 4 altos be selected from 7 sopranos and 9 altos?
How many ways can a committee of 4 people be selected from a group of 10 people?
If 85% of all people have brown eyes and 6 people are selected at random, find the probability that at least 1 of them has brown eyes.
A single die is rolled 4 times. Find the probability of getting at least one 5.
When a meteorologist says that there is a 30% chance of showers, what type of probability is the person using?a. Classicalb. Empirical c. Relatived. Subjective
A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. Disregarding size, how many different hats can be made?
At a convention there are 7 mathematics instructors, 5 computer science instructors, 3 statistics instructors, and 4 science instructors. If an instructor is selected, find the probability of getting a science instructor or a math instructor.
The probability that a person owns a car is 0.80, that a person owns a boat is 0.30, and that a person owns both a car and a boat is 0.12. Find the probability that a person owns either a boat or a car.
The probability that an event happens is 0.42. What is the probability that the event won’t happen?a. 0.42b. 0.58 c. 0d. 1
When objects are arranged in a specific order, the arrangement is called a combination.
The data show the U.S. population by age. Under 20 years 27.0% 20 years and over 73.0 65 years and over 13.1 Choose one person from the United States at random. Find the probability that the person isa. From 20 years to 64 yearsb. Under 20 or 65 and overc. Not 65 and over
The arrangement ABC is the same as BAC for combinations.
If 50 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win 2 prizes if that person buys 2 tickets.
Eight dogs are selected for the final round of a dog show to compete for best of show. How many different ways can they line up to enter the ring? The judge then randomly chooses the dogs to parade around the ring in a circle. In how many ways can this be done?
In 2010 about 69.6% of fulltime law enforcement workers were sworn officers, and of those, 88.2% were male. Females, however,make up 60.8% of civilian employees. Choose one law enforcement worker at random and find the following.a. The probability that she is a female sworn officerb. The
Cheap Rentals has nothing but budget cars for rental. The probability that a car has air conditioning is 0.5, and the probability that a car has a CD player is 0.37. The probability that a car has both air conditioning and a CD player is 0.06. What is the probability that a randomly selected car
If two events are dependent, they must have the same probability of occurring.
Consider the U.S. Senate. Find out about the composition of any three of the Senate’s standing committees. How many different committees of Senators are possible, knowing the party composition of the Senate and the number of committee members from each party for each committee?
At a particular fitness center, 64.1% of the members take at least one class, 18.6% work with a personal trainer, and 9.2% do both. If a member of the center is selected at random, what is the probability that she does neither?
When two events are not mutually exclusive, P(A or B) = P(A) + P(B).
Assume that the gender distribution of babies is such that one-half the time females are born and one-half the time males are born. In a family of 3 children, what is the probability that all are girls? In a family of 4? Is it unusual that in a family with 4 children all would be girls? In a family
We know that if the probability of an event happening is 100%, then the event is a certainty. Can it be concluded that if there is a 50% chance of contracting a communicable disease through contact with an infected person, there would be a 100% chance of contracting the disease if 2 contacts were
What are equally likely events?
In classical probability, all outcomes in the sample space are equally likely.
A music player or music organization program can keep track of how many different artists are in a library. First note how many different artists are in your music library. Then find the probability that if 25 songs are selected at random, none will have the same artist.
How many people do you think need to be in a room so that 2 people will have the same birthday (month and day)?You might think it is 366. This would, of course, guarantee it (excluding leap year), but how many people would need to be in a room so that there would be a 90% probability that 2 people
How many different ways can 6 different video game cartridges be arranged on a shelf?
Classical probability uses a frequency distribution to compute probabilities.
When poker games are shown on television, there are often percentages displayed that show how likely it is that a certain hand will win. Investigate how these percentages are determined. Show an example with two competing hands in a Texas Hold ’Em game. Include the percentages that each hand will
Chevalier de Méré won money when he bet unsuspecting patrons that in 4 rolls of 1 die, he could get at least one 6; but he lost money when he bet that in 24 rolls of 2 dice, he could get at least a double 6. Using the probability rules, find the probability of each event and explain why he won
Define sample space.
Subjective probability has little use in the real world.
Select a pizza restaurant and a sandwich shop. For the pizza restaurant look at the menu to determine how many sizes, crust types, and toppings are available. How many different pizza types are possible? For the sandwich shop determine how many breads, meats, veggies, cheeses, sauces, and
A con man has 3 coins. One coin has been specially made and has a head on each side. A second coin has been specially made, and on each side it has a tail. Finally, a third coin has a head and a tail on it. All coins are of the same denomination. The con man places the 3 coins in his pocket,
What is a probability experiment?
The national average for mathematics SATs in 2011 was 514. Suppose that the distribution of scores was approximately bell-shaped and that the standard deviation was approximately 40. Within what boundaries would you expect 68% of the scores to fall? What percentage of scores would be above 594?
A useful mean in the physical sciences (such as voltage) is the quadratic mean (QM), which is found by taking the square root of the average of the squares of each value. The formula isThe quadratic mean of 3, 5, 6, and 10 isFind the quadratic mean of 8, 6, 3, 5, and 4. QM = Σχ n
The first column of these data represents the prebuy gas price of a rental car, and the second column represents the price charged if the car is returned without refilling the gas tank for a selected car rental company. Draw two boxplots for the data and compare the distributions. Prebuy
A student scored 76 on a general science test where the class mean and standard deviation were 82 and 8, respectively; he also scored 53 on a psychology test where the class mean and standard deviation were 58 and 3, respectively. In which class was his relative position higher?
Check each data set for outliers.a. 88, 72, 97, 84, 86, 85, 100b.145, 119, 122, 118, 125, 116c. 14, 16, 27, 18, 13,
If the range of a data set is 18, estimate the standard deviation of the data.
The average national SAT score is 1019. If we assume a bell-shaped distribution and a standard deviation equal to 110, what percentage of scores will you expect to fall above 1129? Above 799?
Eleven major earthquakes had Richter magnitudes as shown. Find the first and third quartiles for the data.7.0, 6.2, 7.7, 8.0, 6.4, 6.2, 7.2, 5.4, 6.4, 6.5, 7.2
The average number of newspapers for sale in an airport newsstand is 56 with a standard deviation of 6. The average number of newspapers for sale in a convenience store is 44 with a standard deviation of 5. Which data set is more variable?
The data show the number of sheep in the top 12 major sheep-producing states. Find the first and third quartiles for the data. Arizona 160,000 California 610,000 Colorado 375,000 Idaho 220,000 Montana 255,000 Nevada 75,000 New
In an advertisement, a retail store stated that its employees averaged 9 years of service. The distribution is shown here.Using the weighted mean, calculate the correct average. Number of employees 823 Years of service 2 6 10
A random selection of state gasoline taxes per gallon is given below. Find the first and third quartile values for the data.16 18 35.3 25 23.5 27.1 32.5 16 2217.5 19
The distribution of the number of errors that 10 students made on a typing test is shown.Find each of these.a. Mean b. Modal class c. Varianced. Standard deviation Errors 0-2 3-5 6-8 9-11 12-14 Frequency 1 34 1 1
The number of highway miles per gallon of the 10 worst vehicles is shown.12 15 13 14 15 16 17 16 17 18Find each of these.a. Mean e. Rangeb. Median f. Variancec. Mode g.
The data show the number of murders in 25 selected cities. Find the variance and standard deviation for the data. Class limits 34-96 97-159 160-222 223-285 286-348 349-411 412-474 475-537 538-600 Frequency 13 2 0 5 1 1 0 1 2
Find the percentile rank for each value in the data set. The data represent the values in billions of dollars of the damage of 10 hurricanes.1.1, 1.7, 1.9, 2.1, 2.2, 2.5, 3.3, 6.2, 6.8,
If the mode is to the left of the median and the mean is to the right of the median, then the distribution is _________ skewed.
The reported high temperatures of 23 cities of the United States in October are shown. Find the z values fora. A temperature of 80ºb. A temperature of 56º62 72 66 79 83 61 62 85 72
When the sum of the lowest data value and the highest data value is divided by 2, the measure is called the _________.
Research the famous Monty Hall probability problem. Conduct a simulation of the Monty Hall problem online using a simulation program or in class using live “contestants.” After 50 simulations compare your results to those stated in the research you did. Did your simulation support the
In a certain high-risk group, the chances of a person having suffered a heart attack are 55%. If 6 people are chosen, find the probability that at least 1 will have had a heart attack.
At a large factory, the employees were surveyed and classified according to their level of education and whether they attend a sports event at least once a month. The data are shown in the table.If an employee is selected at random, find the probability thata. The employee attends sports events
Evaluate each expression.a. 3C0b. 3C3c. 9C7d. 12C2e. 4C3
The following foreign adoptions (in the United States) occurred during these particular years.Choose one adoption at random from this chart.a. What is the probability that it was from Ethiopia given that it was from 2010?b. What is the probability that it was from Russia and in 2006?c. What is the
In 2010 in the United States, there were 49,904,000 people not covered by health insurance. The numbers of those not covered in selected states are shown below (numbers in thousands.)CA 7209 FL 3854 TX 6181 NY 2886Choose a person not covered by health
The probability that Mike has to work overtime and it rains is 0.028. Mike hears the weather forecast, and there is a 50% chance of rain. Find the probability that he will have to work overtime, given that it rains.
Of the members of the Spring Lake Bowling Lanes, 57% have a lifetime membership and bowl regularly (three or more times a week). If 70% of the club members bowl regularly, find the probability that a randomly selected member is a lifetime member, given that he or she bowls regularly.
The total arrests for property crimes in the United States in a recent year were itemized as follows.Larceny/theft 1,334,933Burglary 299,351Motor
The probability that a customer will buy a new car and an extended warranty is 0.16. If the probability that a customer will purchase a new car is 0.30, find the probability that the customer will also purchase the extended warranty
The top 10 names for boys in America in the 1880s were John, William, Charles, George, James, Frank, Joseph, Harry, Henry, and Edward. The top 10 names for boys in the 1980s were Michael, Christopher, Matthew, Joshua, David, Daniel, James, John, Robert, and Brian. In how many ways can you choose 5
The probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35. If the probability that she is accepted by the college is 0.65, find the probability that she will obtain a scholarship given that she is accepted by the college.
Five cards are drawn from an ordinary deck without replacement. Find the probability of gettinga. All red cardsb. All diamondsc. All aces
Of the physics graduates of a university, 30% received a starting salary of $30,000 or more. If 5 of the graduates are selected at random, find the probability that all had a starting salary of $30,000 or more.
In a game of craps, a player loses on the roll if a 2, 3, or 12 is tossed on the first roll. Find the probability of losing on the first roll.
The probability that a person owns a microwave oven is 0.75, that a person owns a compact disk player is 0.25, and that a person owns both a microwave and a CD player is 0.16. Find the probability that a person owns either a microwave or a CD player, but not both.
A breakdown of the sources of energy used in the United States is shown below. Choose one energy source at random. Find the probability that it isa. Not oilb. Natural gas or oilc. NuclearOil 39% Natural gas 24% Coal 23%Nuclear 8%
Three dice are rolled. Find the probability of gettinga. Triples b. A sum of 5
When 2 dice are rolled, find the probability of gettinga. A sum of 6 or 7b. A sum greater than 8c. A sum less than 3 or greater than 8d. A sum that is divisible by 3e. A sum of 16f. A sum less than 11
Eighty-one percent of U.S. households have DVD players. Choose 6 households at random. What is the probability that at least 1 does not have a DVD player?
U.S. growers harvested 11 billion bushels of corn in 2005. About 1.9 billion bushels were exported, and 1.6 billion bushels were used for ethanol. Choose one bushel of corn at random. What is the probability that it was used either for export or for ethanol?
At a men’s clothing store, 12 men purchased blue golf sweaters, 8 purchased green sweaters, 4 purchased gray sweaters, and 7 bought black sweaters. If a customer is selected at random, find the probability that he purchaseda. A blue sweaterb. A green or gray sweaterc. A green or black or
When two dice are rolled, the sample space consists of how many events?a. 6b. 12 c. 36d. 54
The complement of guessing 5 correct answers on a 5-question true/false exam isa. Guessing 5 incorrect answersb. Guessing at least 1 incorrect answerc. Guessing at least 1 correct answerd. Guessing no incorrect answers
Classify each statement as an example of classical probability, empirical probability, or subjective probability.a. The probability that a person will watch the 6 o’clock evening news is 0.15.b. The probability of winning at a Chuck-a-Luck game is 5/36 .c. The probability that a bus will be in an
The sample space for tossing 3 coins consists of how many outcomes?a. 2b. 4 c. 6d. 8
A probability experiment is conducted. Which of these cannot be considered a probability outcome?a. 2/3b. 0.63 c. -3/5d. 1.65e. -0.44f. 0 g. 1h. 125%i. 24%
When a card is drawn from a deck, find the probability of gettinga. A diamondb. A 5 or a heartc. A 5 and a heartd. A kinge. A red card
When a card is drawn, find the probability of gettinga. A jack b. A 4c. A card less than 6 (an ace is considered above 6)
Of all the murder victims in 2010 whose relation to the offender was known, 24.8% were killed by a family member and 53% by an acquaintance. The rest were killed by a stranger. What is the probability that a randomly selected murder victim was killed by a stranger?
When two events cannot occur at the same time, they are said to be ________.
The sum of the probabilities of the events in the sample space is ________.
The set of all possible outcomes of a probability experiment is called the ________.
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