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mathematics
statistics

Introductory Statistics 8th Edition Prem S. Mann - Solutions

Prepare a box-and-whisker plot for the following data:Does this data set contain any outliers?
Multiple choice questions: 1. The value of the middle term in a ranked data set is called the a. Mean b. Median c. Mode 2. Which of the following summary measures is/are influenced by extreme values? a. Mean b. Median c. Mode d. Range 3. Which of the following summary measures can be calculated for
The following data give the number of items purchased by each of 14 customers who shopped on a certain day at a supermarket.Calculate the mean, median, mode, range, variance, and standard deviation.
The mean, as a measure of central tendency, has the disadvantage of being influenced by extreme values. Illustrate this point with an example.
The range, as a measure of spread, has the disadvantage of being influenced by extreme values. Illustrate this point with an example.
When is the value of the standard deviation for a data set zero? Give one example of such a data set. Calculate the standard deviation for that data set to show that it is zero.
The following table gives the frequency distribution of the numbers of computers sold during the past 25 weeks at an electronics store. Computers Sold Frequency4 to 9............ 210 to 15........... 416 to 21........... 1022 to 27........... 628 to 33........... 3a. What
The members of a very large health club were observed on a randomly selected day. The distribution of times they spent that day at the health club was found to have a mean of 91.8 minutes and a standard deviation of 16.2 minutes. Suppose these values of the mean and standard deviation hold true for
The ages of cars owned by all people living in a city have a bell-shaped distribution with a mean of 7.3 years and a standard deviation of 2.2 years.a. Using the empirical rule, find the percentage of cars in this city that arei. 5.1 to 9.5 years oldii. .7 to 13.9 years oldb. Using the empirical
The following data give the number of times the metal detector was set off by passengers at a small airport during 15 consecutive half-hour periods on February 1, 2012.a. Calculate the three quartiles and the interquartile range. Where does the value of 4 lie in relation to these quartiles?b. Find
Make a box-and-whisker plot for the data on the number of times passengers set off the airport metal detector given in Problem 22. Comment on the skewness of this data set.
The mean weekly wages of a sample of 15 employees of a company are $1035. The mean weekly wages of a sample of 20 employees of another company are $1090. Find the combined mean for these 35 employees.
The mean GPA of five students is 3.21. The GPAs of four of these five students are, respectively, 3.85, 2.67, 3.45, and 2.91. Find the GPA of the fifth student.
The following are the prices (in thousands of dollars) of 10 houses sold recently in a city:Calculate the 10% trimmed mean for this data set. Do you think the 10% trimmed mean is a better summary measure than the (simple) mean (i.e., the mean of all 10 values) for these data? Briefly explain why or
Consider the following two data sets.Each value of the second data set is obtained by subtracting 3 from the corresponding value of the first data set.a. Calculate the mean for each of these two data sets. Comment on the relationship between the two means.b. Calculate the standard deviation for
Define the following terms: experiment, outcome, sample space, simple event, and compound event.
Refer to Exercise 4.4. List all the outcomes included in each of the following events. Indicate which are simple and which are compound events. a. Both students suffer from math anxiety. b. Exactly one student suffers from math anxiety. c. The first student does not suffer and the second suffers
Given that A and B are two mutually exclusive events, find P(A or B) for the following. a. P(A) = .38 and P(B) = .59 b. P(A) = .15 and P(B) = .23
Given that A and B are two mutually exclusive events, find P(A or B) for the following. a. P(A) = .71 and P(B) = .03 b. P(A) = .44 and P(B) = .38
As mentioned in Exercise 4.52, a July 21 survey on www.HuffingtonPost.com asked people to choose their favorite junk food from a list of choices. Although the results were not broken down by gender, suppose that the following table represents the results for the 8002 people who responded, assuming
The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2004 and 2008, based on gender and whether or not they graduated.If one of these players is selected at random, find the following probabilities.a. P(female or
Five hundred employees were selected from a city€™s large private companies, and they were asked whether or not they have any retirement benefits provided by their companies. Based on this information, the following two-way classification table was prepared.Suppose one employee is selected at
Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses.Suppose one adult is selected at random from these 2000 adults. Find the following probabilities.a. P(has never shopped on the
A consumer agency randomly selected 1700 flights for two major airlines, A and B. The following table gives the two-way classification of these flights based on airline and arrival time. €œless than 30 minutes late€ includes flights that arrived early or on time.If one flight
Two thousand randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two-way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off,
There is an area of free (but illegal) parking near an inner-city sports arena. The probability that a car parked in this area will be ticketed by police is .35, that the car will be vandalized is .15, and that it will be ticketed and vandalized is .10. Find the probability that a car parked in
Amy is trying to purchase concert tickets online for two of her favorite bands, the Leather Recliners and Double Latte No Foam. She estimates that her probability of being able to get tickets for the Leather Recliners concert is .14, the probability of being able to get tickets for the Double Latte
Refer to Exercise 4.5. List all the outcomes included in each of the following events. Indicate which are simple and which are compound events. a. One person has an iPad and the other does not. b. At least one person has an iPad. c. Not more than one person has an iPad. d. The first person has an
Given that A and B are two mutually exclusive events, find P(A or B) for the following.a. P(A) = .71 and P(B) = .03b. P(A) = .44 and P(B) = .38 Discuss.
The probability that a randomly selected elementary or secondary school teacher from a city is a female is .68, holds a second job is .38, and is a female and holds a second job is .29. Find the probability that an elementary or secondary school teacher selected at random from this city is a female
According to the U.S. Census Bureau’s most recent data on the marital status of the 242 million Americans aged 15 years and older, 124.2 million are currently married and 74.5 million have never been married. If one person from these 242 million persons is selected at random, find the probability
According to a survey of 2000 home owners, 800 of them own homes with three bedrooms, and 600 of them own homes with four bedrooms. If one home owner is selected at random from these 2000 home owners, find the probability that this home owner owns a house that has three or four bedrooms. Explain
According to an Automobile Association of America report, 9.6% of Americans traveled by car over the 2011 Memorial Day weekend and 88.09% stayed home. What is the probability that a randomly selected American stayed home or traveled by car over the 2011 Memorial Day weekend? Explain why this
Twenty percent of a town’s voter’s favor letting a major discount store move into their neighborhood, 63% is against it, and 17% are indifferent. What is the probability that a randomly selected voter from this town will either be against it or be indifferent? Explain why this probability is
The probability that a corporation makes charitable contributions is .72. Two corporations are selected at random, and it is noted whether or not they make charitable contributions.a. Draw a tree diagram for this experiment.b. Find the probability that at most one corporation makes charitable
The probability that an open-heart operation is successful is .84. What is the probability that in two randomly selected open-heart operations at least one will be successful? Draw a tree diagram for this experiment.
Refer to Exercise 4.6. List all of the outcomes in each of the following events and mention which of these are simple and which are compound events. a. Exactly one customer receives $20 bills. b. Both customers receive $10 bills. c. At most one customer receives $20 bills. d. The first customer
Determine the value of each of the following using the appropriate formula.
Find the value of each of the following using the appropriate formula.
A ski patrol unit has nine members available for duty, and two of them are to be sent to rescue an injured skier. In how many ways can two of these nine members be selected? Now suppose the order of selection is important. How many arrangements are possible in this case?
An ice cream shop offers 25 flavors of ice cream. How many ways are there to select 2 different flavors from these 25 flavors? How many permutations are possible?
A veterinarian assigned to a racetrack has received a tip that one or more of the 12 horses in the third race have been doped. She has time to test only 3 horses. How many ways are there to randomly select 3 horses from these 12 horses? How many permutations are possible?
An environmental agency will randomly select 4 houses from a block containing 25 houses for a radon check. How many total selections are possible? How many permutations are possible?
Refer to Exercise 4.7. List all the outcomes included in each of the following events. Indicate which are simple and which are compound events. a. At least one part is good. b. Exactly one part is defective. c. The first part is good and the second is defective. d. At most one part is good.
An investor will randomly select 6 stocks from 20 for an investment. How many total combinations are possible? If the order in which stocks are selected is important, how many permutations will there be?
A company employs a total of 16 workers. The management has asked these employees to select 2 workers who will negotiate a new contract with management. The employees have decided to select the 2 workers randomly. How many total selections are possible? Considering that the order of selection is
In how many ways can a sample (without replacement) of 9 items be selected from a population of 20 items?
In how many ways can a sample (without replacement) of 5 items be selected from a population of 15 items?
A car rental agency currently has 44 cars available, 28 of which have a GPS navigation system. One of the 44 cars is selected at random. Find the probability that this car a. Has a GPS navigation system b. Does not have a GPS navigation system
A random sample of 250 juniors majoring in psychology or communication at a large university is selected. These students are asked whether or not they are happy with their majors. The following table gives the results of the survey. Assume that none of these 250 students is majoring in both
A random sample of 250 adults was taken, and they were asked whether they prefer watching sports or opera on television. The following table gives the two-way classification of these adults.a. If one adult is selected at random from this group, find the probability that this adult i. Prefers
A random sample of 80 lawyers was taken, and they were asked if they are in favor of or against capital punishment. The following table gives the two-way classification of their responses.a. If one lawyer is randomly selected from this group, find the probability that this lawyer i. Favors capital
A random sample of 400 college students was asked if college athletes should be paid. The following table gives a two-way classification of the responses.a. If one student is randomly selected from these 400 students, find the probability that this student i. Is in favor of paying college
Refer to Exercise 4.8. List all the outcomes included in each of the following events and mention which are simple and which are compound events. a. At most one person is against a tax increase on rich people. b. Exactly two persons are in favor of a tax increase on rich people. c. At least one
An appliance repair company that makes service calls to customers’ homes has found that 5% of the time there is nothing wrong with the appliance and the problem is due to customer error (appliance unplugged, controls improperly set, etc.). Two service calls are selected at random, and it is
According to the National Science Foundation, during the Fall 2008 semester (the most recent data available) 30.13% of all science and engineering graduate students enrolled in doctorate granting colleges in the United States were temporary visa holders
Refer to Exercise 4.134. Two cars are selected at random from these 44 cars. Find the probability that both of these cars have GPS navigation systems.
Refer to Exercise 4.135. Two students are selected at random from this class of 35 students. Find the probability that the first student selected is a junior and the second is a sophomore.
A company has installed a generator to back up the power in case there is a power failure. The probability that there will be a power failure during a snowstorm is .30. The probability that the generator will stop working during a snowstorm is .09. What is the probability that during a snowstorm
A player plays a roulette game in a casino by betting on a single number each time. Because the wheel has 38 numbers, the probability that the player will win in a single play is 1/38. Each play of the game is independent of all previous plays. a. Find the probability that the player will win for
A certain state’s auto license plates have three letters of the alphabet followed by a three-digit number.a. How many different license plates are possible if all three-letter sequences are permitted and any number from 000 to 999 is allowed?b. Arnold witnessed a hit-and-run accident. He knows
The median life of Brand LT5 batteries is 100 hours. What is the probability that in a set of three such batteries, exactly two will last longer than 100 hours?
Powerball is a game of chance that has generated intense interest because of its large jackpots. To play this game, a player selects five different numbers from 1 through 59, and then picks a Powerball number from 1 through 39. The lottery organization randomly draws 5 different white balls from 59
Briefly explain the two properties of probability.
A trimotor plane has three engines—a central engine and an engine on each wing. The plane will crash only if the central engine fails and at least one of the two wing engines fails. The probability of failure during any given flight is .005 for the central engine and .008 for each of the wing
A box contains 10 red marbles and 10 green marbles. a. Sampling at random from this box five times with replacement, you have drawn a red marble all five times. What is the probability of drawing a red marble the sixth time? b. Sampling at random from this box five times without replacement, you
A gambler has four cards—two diamonds and two clubs. The gambler proposes the following game to you: You will leave the room and the gambler will put the cards face down on a table. When you return to the room, you will pick two cards at random. You will win $10 if both cards are diamonds, you
A thief has stolen Roger’s automatic teller machine (ATM) card. The card has a four-digit personal identification number (PIN). The thief knows that the first two digits are 3 and 5, but he does not know the last two digits. Thus, the PIN could be any number from 3500 to 3599. To protect the
Consider the following games with two dice. a. A gambler is going to roll a die four times. If he rolls at least one 6, you must pay him $5. If he fails to roll a 6 in four tries, he will pay you $5. Find the probability that you must pay the gambler. Assume that there is no cheating. b. The same
A gambler has given you two jars and 20 marbles. Of these 20 marbles, 10 are red and 10 are green. You must put all 20 marbles in these two jars in such a way that each jar must have at least one marble in it. Then a friend of yours, who is blindfolded, will select one of the two jars at random and
A screening test for a certain disease is prone to giving false positives or false negatives. If a patient being tested has the disease, the probability that the test indicates a (false) negative is .13. If the patient does not have the disease, the probability that the test indicates a (false)
A pizza parlor has 12 different toppings available for its pizzas, and 2 of these toppings are pepperoni and anchovies. If a customer picks 2 toppings at random, find the probability thata. Neither topping is anchoviesb. Pepperoni is one of the toppings
An insurance company has information that 93% of its auto policy holders carry collision coverage or uninsured motorist coverage on their policies. Eighty percent of the policy holders carry collision coverage, and 60% have uninsured motorist coverage.a. What percentage of these policy holders
Many states have a lottery game, usually called a Pick-4, in which you pick a four-digit number such as 7359. During the lottery drawing, there are four bins, each containing balls numbered 0 through 9. One ball is drawn from each bin to form the four-digit winning number. a. You purchase one
Briefly describe an impossible event and a sure event. What is the probability of the occurrence of each of these two events?
A restaurant chain is planning to purchase 100 ovens from a manufacturer, provided that these ovens pass a detailed inspection. Because of high inspection costs, 5 ovens are selected at random for inspection. These 100 ovens will be purchased if at most 1 of the 5 selected ovens fails inspection.
A production system has two production lines; each production line performs a two-part process, and each process is completed by a different machine. Thus, there are four machines, which we can identify as two first-level machines and two second-level machines. Each of the first-level machines
The Big Six Wheel (or Wheel of Fortune) is a casino and carnival game that is well known for being a big money maker for the casinos. The wheel has 54 equally likely slots (outcomes) on it. The slot that pays the largest amount of money is called the joker. If a player bets on the joker, the
A Wired Equivalent Privacy (WEP) key is a security code that one must enter in order to access a secure WiFi network. The characters in the key are used from the numbers 0 to 9 and letters from A to F, which gives 16 possibilities for each character of the key. Repeats are allowed, that is, the
A large university has 12,600 male students. Of these students, 5312 are members of so-called “Greek” social organizations (fraternities or sororities), 2844 are members of Greek service organizations, and the others are not members of either of these two types of Greek organizations.
Briefly explain the three approaches to probability. Give one example of each approach.
List the simple events for each of the following statistical experiments in a sample space S. a. One roll of a die b. Three tosses of a coin c. One toss of a coin and one roll of a die
Suppose a randomly selected passenger is about to go through the metal detector at JFK Airport in New York City. Consider the following two outcomes: The passenger sets off the metal detector, and the passenger does not set off the metal detector. Are these two outcomes equally likely? Explain why
Fifty-six people have signed up for a karaoke contest at a local nightclub. Of them, 19 sang in a band, chorus, or choir while in high school and 37 did not. Suppose one contestant is chosen at random. Consider the following two events: The selected contestant sang in a band, chorus, or choir while
The television game show The Price Is Right has a game called the Shell Game. The game has four shells, and one of these four shells has a ball under it. The contestant chooses one shell. If this shell contains the ball, the contestant wins. If a contestant chooses one shell randomly, what is the
There are 1265 eligible voters in a town, and 972 of them are registered to vote. If one eligible voter is selected at random from this town, what is the probability that this voter isa. Registered?b. Not registered?Do these two probabilities add up to 1.0? If yes, why?
According to an article in The Sacramento Bee (www.sacbee.com/2011/08/04/3816872/medicareprescription- premiums.html), approximately 10% of Medicare beneficiaries lack a prescription drug care plan. Suppose that a town in Florida has 2384 residents who are Medicare beneficiaries, and 216 of them do
A sample of 500 large companies showed that 120 of them offer free psychiatric help to their employees who suffer from psychological problems. If one company is selected at random from this sample, what is the probability that this company offers free psychiatric help to its employees who suffer
A sample of 400 large companies showed that 130 of them offer free health fitness centers to their employees on the company premises. If one company is selected at random from this sample, what is the probability that this company offers a free health fitness center to its employees on the company
In a large city, 15,000 workers lost their jobs last year. Of them, 7400 lost their jobs because their companies closed down or moved, 4600 lost their jobs due to insufficient work, and the remainder lost their jobs because their positions were abolished. If one of these 15,000 workers is selected
Many colleges require students to take a placement exam to determine which math courses they are eligible to take during the first semester of their freshman year. Of the 2938 freshmen at a local state college, 214 were required to take a remedial math course, 1465 could take a nonremedial,
In a sample of 500 families, 70 have a yearly income of less than $40,000, 220 have a yearly income of $40,000 to $80,000, and the remaining families have a yearly income of more than $80,000. Write the frequency distribution table for this problem. Calculate the relative frequencies for all
Two students are randomly selected from a statistics class, and it is observed whether or not they suffer from math anxiety. How many total outcomes are possible? Draw a tree diagram for this experiment. Draw a Venn diagram.
Briefly explain the difference between the marginal and conditional probabilities of events. Give one example of each.
Briefly explain the meaning of independent and dependent events. Suppose A and B are two events. What formula will you use to prove whether A and B are independent or dependent?
A statistical experiment has 11 equally likely outcomes that are denoted by a, b, c, d, e, f, g, h, i, j, and k. Consider three events: A = {b, d, e, j}, B = {a, c, f, j}, and C = {c, g, k}.a. Are events A and B independent events? What about events A and C?b. Are events A and B mutually exclusive
A statistical experiment has 10 equally likely outcomes that are denoted by 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Let event A = {3, 4, 6, 9} and event B = {1, 2, 5}.a. Are events A and B mutually exclusive events?b. Are events A and B independent events?c. What are the complements of events A and B,
Two thousand randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses.a. If one adult is selected at random from these 2000 adults, find the probability that this adult i. Has never shopped on the
A 2010€“2011 poll conducted by Gallup, (www.gallup.com/poll/148994/Emotional-Health Higher- Among-Older-Americans.aspx) examined the emotional health of a large number of Americans. Among other things, Gallup reported on whether people had an Emotional Health Index score of 90 or higher,
Two thousand randomly selected adults were asked if they are in favor of or against cloning. The following table gives the responses.a. If one person is selected at random from these 2000 adults, find the probability that this person is i. In favor of cloning ii. Against cloning iii. In favor of

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