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business statistics using excel
Introductory Statistics 7th Edition Prem S Mann - Solutions
5.24 Find the mean and standard deviation for each of the following probability distributions.a.x P(x) b.x P(x)3 .09 0 .43 4 .21 1 .31 5 .34 2 .17 6 .23 3 .09 7 .13
5.23 Find the mean and standard deviation for each of the following probability distributions.a.x P(x) b.x P(x)0 .16 6 .40 1 .27 7 .26 2 .39 8 .21 3 .18 9 .13
5.22 Briefly explain the concept of the mean and standard deviation of a discrete random variable.
*5.21 In a group of 20 athletes, 6 have used performance-enhancing drugs that are illegal. Suppose that 2 athletes are randomly selected from this group. Let x denote the number of athletes in this sample who have used such illegal drugs. Write the probability distribution of x. You may draw a tree
*5.20 In a group of 12 persons, 3 are left-handed. Suppose that 2 persons are randomly selected from this group. Let x denote the number of left-handed persons in this sample. Write the probability distribution of x. You may draw a tree diagram and use it to write the probability distribution.
5.19 In a 2006 ABC News poll, 37% of adult Americans stated that they encounter “rude and disrespectful behavior” often (Source: http://abcnews.go.com/images/Politics/1005a1HowRude.pdf). Suppose that this result holds true for the current population of adult Americans. Suppose that two adult
5.18 According to a survey, 30% of adults are against using animals for research. Assume that this result holds true for the current population of all adults. Let x be the number of adults who are against using animals for research in a random sample of two adults. Obtain the probability
5.17 In the 2008 Beach to Beacon 10K run, 27.4% of the 5248 participants finished the race in 49 minutes 42 seconds (49:42) or faster, which is equivalent to a pace of less than 8 minutes per mile (Source:http://www.beach2beacon.org/b2b_2008_runners.htm). Suppose that this result holds true for all
5.16 Five percent of all cars manufactured at a large auto company are lemons. Suppose two cars are selected at random from the production line of this company. Let x denote the number of lemons in this sample.Write the probability distribution of x. Draw a tree diagram for this problem.
5.15 One of the most profitable items at A1’s Auto Security Shop is the remote starting system. Let x be the number of such systems installed on a given day at this shop. The following table lists the frequency distribution of x for the past 80 days.x 1 2 3 4 5 f 8 20 24 16 12a. Construct a
5.14 The H2 Hummer limousine has eight tires on it. A fleet of 1300 H2 limos was fit with a batch of tires that mistakenly passed quality testing. The following table lists the frequency distribution of the number of defective tires on the 1300 H2 limos.Number of defective tires 0 1 2 3 4 5 6 7 8
5.13 Nathan Cheboygan, a singing gambler from northern Michigan, is famous for his loaded dice. The following table shows the probability distribution for the sum, denoted by x, of the faces on a pair of Nathan’s dice.x 2 3 4 5 6 7 8 9 10 11 12 P(x) .065 .065 .08 .095 .11 .17 .11 .095 .08 .065
5.12 A review of emergency room records at rural Millard Fellmore Memorial Hospital was performed to determine the probability distribution of the number of patients entering the emergency room during a 1-hour period. The following table lists the distribution.Patients per hour 0 1 2 3 4 5 6
5.11 The following table gives the probability distribution of a discrete random variable x.x 0 1 2 3 4 5 P(x) .03 .17 .22 .31 .15 .12 Find the following probabilities.a. P(x 1)b. P(x 1)c. P(x 3)d. P(0 x 2)e. Probability that x assumes a value less than 3f. Probability that x assumes a
5.10 The following table gives the probability distribution of a discrete random variable x.x 0 1 2 3 4 5 6 P(x) .11 .19 .28 .15 .12 .09 .06 Find the following probabilities.a. P(x 3)b. P(x 2)c. P(x 4)d. P(1 x 4)e. Probability that x assumes a value less than 4f. Probability that x
5.9 Each of the following tables lists certain values of x and their probabilities. Determine whether or not each one satisfies the two conditions required for a valid probability distribution.a. x P(x) b.x P(x)c. x P(x)5 .36 1 .27 0 .15 6 .48 2 .24 1 .08 7 .62 3 .49 2 .20 8 .26 3 .50
5.8 Each of the following tables lists certain values of x and their probabilities. Verify whether or not each represents a valid probability distribution.a. x P(x) b.x P(x) c.x P(x)0 .10 2 .35 7 .25 1 .05 3 .28 8 .85 2 .45 4 .20 9 .40 3 .40 5 .14
5.7 Briefly explain the two characteristics (conditions) of the probability distribution of a discrete random variable.
5.6 Explain the meaning of the probability distribution of a discrete random variable. Give one example of such a probability distribution. What are the three ways to present the probability distribution of a discrete random variable?
5.5 One of the four gas stations located at an intersection of two major roads is a Texaco station. Suppose the next six cars that stop at any of these four gas stations make their selections randomly and independently. Let x be the number of cars in these six that stop at the Texaco station. Is x
5.4 A household can watch news on any of the three networks—ABC, CBS, or NBC. On a certain day, five households randomly and independently decide which channel to watch. Let x be the number of households among these five that decide to watch news on ABC. Is x a discrete or a continuous random
5.3 Indicate which of the following random variables are discrete and which are continuous.a. The number of new accounts opened at a bank during a certain monthb. The time taken to run a marathonc. The price of a concert ticketd. The number of times a person says “please” in a daye. The points
5.2 Classify each of the following random variables as discrete or continuous.a. The time left on a parking meterb. The number of bats broken by a major league baseball team in a seasonc. The number of cars in a parking lotd. The total pounds of fish caught on a fishing tripe. The number of cars
5.1 Explain the meaning of a random variable, a discrete random variable, and a continuous random variable.Give one example each of a discrete random variable and a continuous random variable.
TA4.3 Random number generators can be used to simulate the behavior of many different types of events, including those that have an infinite set of possibilities.a. Generate a set of 200 random numbers on the interval 0 to 1 and save them to a column or list in the technology you are using.b.
TA4.2 You want to simulate the rolling of a die. Assign the values 1 through 6 to the outcomes from 1-spot through 6-spots on the die, respectively.a. Simulate 200 rolls of the die by generating 200 random (integer) numbers between 1 and 6. Then make a histogram for these 200 numbers.b. Repeat part
TA4.1 You want to simulate the tossing of a coin. Assign a value of 0 (zero) to Head and a value of 1 to Tail.a. Simulate 50 tosses of the coin by generating 50 random (integer) numbers between 0 and 1. Then calculate the mean of these 50 numbers. This mean gives you the proportion of 50 tosses
20. A sample was selected of 506 workers who currently receive two weeks of paid vacation per year.These workers were asked if they were willing to accept a small pay cut to get an additional week of paid vacation a year. The following table shows the responses of these workers.Yes No No Response
19. The probability that a randomly selected student from a college is a female is .55 and the probability that a student works for more than 10 hours per week is .62. If these two events are independent, find the probability that a randomly selected student is aa. male and works for more than 10
18. A hat contains five green, eight red, and seven blue marbles. Let A be the event that a red marble is drawn if we randomly select one marble out of this hat. What is the probability of A? What is the complementary event of A, and what is its probability?
17. The probability that an adult has ever experienced a migraine headache is .35. If two adults are randomly selected, what is the probability that neither of them has ever experienced a migraine headache?
16. Reconsider Problem 14. If two of these 200 students are selected at random, what is the probability that both of them are out-of-state students?
15. Reconsider Problem 14. If one of these 200 students is selected at random, what is the probability that the selected student is a female or an out-of-state student?
14. There are 200 students in a particular graduate program at a state university. Of them, 110 are female and 125 are out-of-state students. Of the 110 females, 70 are out-of-state students.a. Are the events “female” and “out-of-state student” independent? Are they mutually exclusive?
13. Lucia graduated this year with an accounting degree from Eastern Connecticut State University. She has received job offers from an accounting firm, an insurance company, and an airline. She cannot decide which of the three job offers she should accept. Suppose she decides to randomly select one
12. A couple is planning their wedding reception. The bride’s parents have given them a choice of four reception facilities, three caterers, five DJs, and two limo services. If the couple randomly selects one reception facility, one caterer, one DJ, and one limo service, how many different
11. Two independent events area. always mutually exclusiveb. never mutually exclusivec. always complementary
10. The joint probability of two mutually exclusive events is alwaysa. 1.0b. between 0 and 1c. 0
9. The sum of the probabilities of all final outcomes of an experiment is alwaysa. 100b. 1.0c. 0
8. The probability of an event is alwaysa. less than 0b. in the range 0 to 1.0c. greater than 1.0
7. Two independent eventsa. have the same probabilityb. cannot occur togetherc. have no effect on the occurrence of each other
6. Two mutually exclusive eventsa. have the same probabilityb. cannot occur togetherc. have no effect on the occurrence of each other
5. Which of the following probability approaches can be applied only to experiments with equally likely outcomes?a. Classical probabilityb. Empirical probabilityc. Subjective probability
4. Two equally likely eventsa. have the same probability of occurrenceb. cannot occur togetherc. have no effect on the occurrence of each other
3. A compound event includesa. all final outcomesb. exactly two outcomesc. more than one outcome for an experiment
2. A final outcome of an experiment is calleda. a compound eventb. a simple eventc. a complementary event
1. The collection of all outcomes for an experiment is calleda. a sample spaceb. the intersection of eventsc. joint probability
4.151 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
4.150 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
4.149 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
4.148 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
4.147 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
4.146 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
4.145 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
4.144 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
4.143 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
4.142 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,
4.141 A box contains 10 red marbles and 10 green marbles.a. Sampling at random from the 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 the box five times without replacement, you
4.140 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
4.139 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
4.138 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?
4.137 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
4.136 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 138. Note that each play of the game is independent of all previous plays.a. Find the probability that the player
4.135 Terry & Sons makes bearings for autos. The production system involves two independent processing machines so that each bearing passes through these two processes. The probability that the first processing machine is not working properly at any time is .08, and the probability that the second
4.134 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
4.133 Refer to Exercise 4.125. 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.
4.132 Refer to Exercise 4.124. Two cars are selected at random from these 44 cars. Find the probability that both of these cars have GPS navigation systems.
4.131 According to the May 2009 issue of U.S. News and World Report, 85.1% of the students who graduated with an MBA degree in 2008 from the University of Virginia’s Darden School of Business had job offers before the graduation date. Suppose that this percentage is true for the top 50 MBA
4.130 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
4.129 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.Should Be Paid Should Not Be Paid Student athlete 90 10 Student nonathlete 210 90a. If one student is randomly selected from these 400
4.128 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.Favors Capital Opposes Capital Punishment Punishment Male 32 24 Female 13 11a. If one lawyer is randomly
4.127 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.Prefer Watching Prefer Watching Sports Opera Male 96 24 Female 45 85a. If one adult is selected at
4.126 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
4.125 In a class of 35 students, 13 are seniors, 9 are juniors, 8 are sophomores, and 5 are freshmen. If one student is selected at random from this class, what is the probability that this student isa. a junior?b. a freshman?
4.124 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 cara. has a GPS navigation systemb. does not have a GPS navigation system
4.123 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.
4.122 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
4.121 Twenty percent of a town’s voters favor letting a major discount store move into their neighborhood, 63% are 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
4.120 The probability of a student getting an A grade in an economics class is .24 and that of getting a B grade is .28. What is the probability that a randomly selected student from this class will get an A or a B in this class? Explain why this probability is not equal to 1.0.
4.119 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
4.118 According to the U.S. Census Bureau’s most recent data on the marital status of the 238 million Americans aged 15 years and older, 123.7 million are currently married and 71.5 million have never been married. If one person from these 238 million persons is selected at random, find the
4.117 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
4.116 Jason and Lisa are planning an outdoor reception following their wedding. They estimate that the probability of bad weather is .25, that of a disruptive incident (a fight breaks out, the limousine is late, etc.)is .15, and that bad weather and a disruptive incident will occur is .08. Assuming
4.115 The probability that a family owns a washing machine is .68, that it owns a DVD player is .81, and that it owns both a washing machine and a DVD player is .58. What is the probability that a randomly selected family owns a washing machine or a DVD player?
4.114 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
4.113 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
4.112 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. Note that “less than 30 minutes late” includes flights that arrived early or on time.Less Than 30 30
4.111 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.Have Shopped Have Never Shopped Male 500 700 Female 300 500 Suppose one adult is selected at random from these 2000
4.110 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.Have Retirement Benefits Yes No
4.109 The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2001 and 2005, based on gender and whether or not they graduated.Graduated Did Not Graduate Male 126 55 Female 133 32 If one of these players is selected
4.108 In a sample survey, 1800 senior citizens were asked whether or not they have ever been victimized by a dishonest telemarketer. The following table gives the responses by age group.Have Been Have Never Victimized Been Victimized 60–69 (A) 106 698 Age 70–79 (B) 145 447 80 or over (C) 61 343
4.107 Given that A and B are two mutually exclusive events, find P(A or B) for the following.a. P(A) .25 and P(B) .27b. P(A) .58 and P(B) .09
4.106 Given that A and B are two mutually exclusive events, find P(A or B) for the following.a. P(A) .47 and P(B) .32b. P(A) .16 and P(B) .59
4.105 Find P(A or B) for the following.a. P(A) .18, P(B) .49, and P(A and B) .11b. P(A) .73, P(B) .71, and P(A and B) .68
4.104 Find P(A or B) for the following.a. P(A) .58, P(B) .66, and P(A and B) .57b. P(A) .72, P(B) .42, and P(A and B) .39
4.103 When is the following addition rule used to find the probability of the union of two events A and B?Give one example where you might use this formula.
4.102 Consider the following addition rule to find the probability of the union of two events A and B:When and why is the term P(A and B) subtracted from the sum of P(A) and P(B)? Give one example where you might use this formula.
4.101 How is the addition rule of probability for two mutually exclusive events different from the rule for two mutually nonexclusive events?
4.100 Explain the meaning of the union of two events. Give one example.
4.99 Suppose that 20% of all adults in a small town live alone, and 8% of the adults live alone and have at least one pet. What is the probability that a randomly selected adult from this town has at least one pet given that this adult lives alone?
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