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24 Cards in this Set

  • Front
  • Back

VisaCard USA studied how frequently young consumers, ages 18 to 24, use plasticcards in making purchases. The results of the study provided the followingprobabilities.




> The probability that aconsumer uses a plastic card when making a purchase is .37.


> Given that the consumeruses a plastic card, there is a .19 probability that the consumer is 18 to 24years old.


> Given that the consumeruses a plastic card, there is .81 probability that the consumer is more than 18to 24 years old.




U.S.Census Bureau data show that 14% of the consumer population is 18 to 24 yearsold.




A. Given that the consumeris 18 to 24 years old, what is the probability that the consumer uses a plasticcard?


B. Given that the consumeris over 24 years old, what is the probability that the consumer uses a plasticcard?


C. What is theinterpretation of the probabilities shown in (A) & (B)?

Ch. 4
Page 193


#37

Jerry Stackhouse of the NBA Dallas Mavericks is the best free throw shooter on the team, making 89% of his shots. Assume that late in a basketball game, Jerry Stackhouse is fouled and is awarded two shots.




A. What is the probability that he will make both shots?


B. What is the probability that he will make at least one shot?


C. What is the probability that he will miss both shots?

Ch. 4


Page 192


#36

Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of he data within' each of the following ranges:




A. 20 to 40


B. 15 to 45


C. 22 to 38


D. 18 to 42


E. 12 to 48

Ch. 3


Page 125


#27

Consider a binomial experiment with n=10 and p= .10. Compute the following:




A. f(0)


B. f(2)


C. P(x less than or equal to 2)


D. P(x is greater than or equal to 1)


E. E(x)


D. Var(x) and St.dev.

Ch. 5


Page 234


#27

In San Francisco, 30% of workers take public transportation daily.



A. In a sample of 10 workers, what is the probability that exactly three workers take public transportation daily?


B. In a sample of 10 workers, what is the probability that at least three workers take public transportation daily?

Ch. 5


Page 234


#29

The US Department of Transportation reported that during November, 83.4% of Southwest Airlines' flights, 75.1% of US Airways' flights, and 70.1% of JetBlue's flights arrived on time. Assumer that this on-time performance is applicable for flights arriving at Concourse A of the Rochester Intl. Airport, and that 40& of the arrivals at CA are Southwest Airlines, 35% are US Airways, and 25% are JetBlue.




B. Flight 1424 will be arriving at gat 20 in CA. What is the most likely airline for this arrival?


C. What is the probability that Flight 1424 will arrive on time?


D. Suppose Flight 1424 will be late. What airline is it most likely? Least likely?

Ch. 4


Page 192


#34

The National Association of Realtors provided data showing that home sales were the slowest in 10 years. Sample data with representative sales prices for existing homes and new homes follow. Data are in the thousands of dollars:




Existing Homes: 315.5, 202.5, 140.2, 181.3, 470.2, 169.9, 112.8, 230.0, 177.5


New Homes: 275.9, 350.2, 195.8, 525.0, 225.3, 215.5, 175.0, 149.5




A. What is the median sales price for existing homes?


B. What is the median sales price for new homes?


C. Do existing homes or new homes have the higher median sales price? What is the difference between the median sales price?


D. A year earlier the median sales for existing homes was $208.4 thousand and the median sales price for new homes was $249 thousand. Compute the percentage change in the median sales price of existing and new homes over the one-year period. Did existing homes or new homes have the larger percentage change in median sales price?

Ch. 3


Page 109


#9

A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons.




A. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons?


B. What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?

Ch. 4


Page 185


#28

The Census Bureau's Current Population Survey shows that 28% of individuals, ages 25 and older, have completed four years of college. For a sample of 15 individuals, ages 25 and older...




A. What is the probability that four will have completed four years of college?


B. What is the probability that three or more will have completed four years of college?

Ch. 5


Page 235


#34

Five observations taken for two variables follow:



Xi 4 6 11 3 16


Yi 50 50 40 60 30




B. Compute and interpret the sample covariance.


C. Compute and interpret the sample correlation coefficient.

Ch. 3


Page 141


#45

Do you think the govt. protects investors adequately? This was part of a survey of investors aged less than 65 living in the United States and Great Britain. The numbers are:




Response United States Great Britain


Yes 187 197


No 334 411


Unsure 256 213




A. Estimate the probability that an investor in the USA thinks the govt. is not protecting investors adequately.


B. Estimate the probability that an investor is Great Britain thinks the government is not protecting investors adequately or is unsure the govt. is protecting them adequately.


C. For a randomly selected investor from these two countries, estimate the probability that the investor thinks the govt. is not protecting investors.


D. Based on the survey results, does there appear to be much difference between the perceptions of investors in the US v. Great Britain regarding the issue of investor protection?

Ch. 4


Page 178


#19

When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.




A. Describe the conditions under which this situation would be a binomial experiment.


C. How many experimental outcomes result in exactly one defect being found?


D. Compute the probabilities associated with finding no defects, exactly one defect, and two defects.

Ch. 5


Page 234


#30

Information about mutual funds by MIR includes the type of mutual fund (Domestic Equity, Intl. Equity, and Fixed Income) and the Morningstar rating for the fund. The rating is expressed from 1-star (low) to 5-star (high). A sample of 25 funds was selected from MF500. The following counts were obtained:


> Sixteen mutual funds were Domestic Equity funds.


> Thirteen mutual funds were rated 3-star or less.


> Seven of the Domestic Equity funds were rated 4-star.


> Two of the Domestic Equity funds were rated 5-star.




Assume that one of these 25 mutual funds will be randomly selected in order to learn more about the mutual fund and its investment strategy.
A. What is the probability of selecting a Domestic Equity fund?


B. What is the probability of selecting a fund with a 4-star or 5-star rating?


C. What is the probability of selecting a fund that is both a Domestic Equity fund and a fund with a 4-star or 5-star rating?


D. What is the probability of selecting a fund that is Domestic Equity fund or a fund with a 4-star or 5-star rating?

Ch. 4


Page 185


#26

Consider a sample with data values of 10, 20, 21, 17, 16, and 12.




Compute the mean and median.

Ch. 3


Page 107


#2

Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53.



Compute the mean, median, and mode.

Ch. 3


Page 107


#4

The U.S. Census Bureau provides data on a the number of young adults, ages 18 to 24, who are living in their parents homes.




M = the event a male young adult is living his parents home


F = the event a female young adult is living in her parents home




If we randomly select a male young adult and a female young adult, the Census Bureau data enable us to conclude P(M) = .56 and P(F) = .42. The probability that both are living are living in their parents' home is .24.




A. What is the probability at least one of the two young adults selected is living in his or her parents' home?


B. What is the probability both young adults selected are living on their own (neither is living in their parents' home)?

Ch. 4


Page 184


#25

The number of students taking the SAT has risen to an all-time high of more than 1.5 million. Students are allowed to repeat the test in hopes of improving the score that is sent out to admissions. The number of times is as follows:




# of Times # of Students


1 721,769


2 601,325


3 166,73


4 22,299


5 6,730




B. What is the probability that a student takes the SAT more than one time?


C. Probability a student takes it more than three times?


D. What is the expected value of the number of times the SAT is taken? What is your interpretation of the expected value?


E. What is the variance and standard deviation of the number of times the SAT is taken?

Ch. 5


Page 222


#17

A bowler's scores for six games were 182, 168, 184, 190, 170, and 174. Using these data as a sample, compute the following descriptive statistics:




A. Range


B. Variance


C. Standard Deviation


D. Coefficient of variation

Ch. 3


Page 118


#16

Car rental rates per day for a sample of seven Eastern U.S. cities are as follows.




City Daily Rate


Boston $43


Atlanta 35


Miami 34


New York 58


Orlando 30


Pittsburgh 30


Washington, D.C. 36




A. Compute the mean, variance, and standard deviation for the car rental rates.


B. A similar sample of seven Western U.S. cities showed a sample mean car rental rate of $38 per day. The variance and standard deviation were 12.3 and 3.5, respectively. Discuss any difference between the car rental rates in Eastern and Western U.S. cities.

Ch. 3


Page 119


#18

The NBA records a variety of statistics for each team. Two of these statistics are the percentage of field goals made by the team and the percentage of three-point shots made by the team. For a portion of the 2004 season, the shooting records of the 29 teams in the NBA showed that the probability of scoring two points by making a field goal was .44, and the probability of scoring three points by making a three-point shot was .34.




A. What is the expected value of a two-point shot for these teams?


B. What is the expected value of a a three-point shot for these teams?


C. If the probability of making a two-point shot is greater than the probability of making a three-point shot, why do coaches allow some players to shoot the three-point shot if they have the opportunity? Use expected value to explain your answer.

Ch. 5


Page 223


#19

The national average for the math portion of the College Board's SAT is 515. The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the verbal test scores.




A. What percentage of students have an SAT math score greater than 615?


B. Greater than 715?


C. Between 415 and 515?


D. Between 315 and 615?

Ch. 3


Page 126


#31

Fortune magazine publishes an annual list of the 500 largest companies in the United States. The following data show the five states with the largest number of Fortune 500 companies.




State # of Companies


New York 54


California 52


Texas 48


Illinois 33


Ohio 30




Suppose F500 company is chosen for a follow-up questionnaire. What are the probabilities of the following events?




A. Find the P(New York).


B. Find the P(Texas).


C. Let B be the event the company is HQ'd in one of these five states. Find P(B).

Ch. 4


Page 179


#20

The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On three of the days only one operating room was used, on five of the days two were used, on eight of the days three were used, and on four days all four of the hospital's operating rooms were used.




A. Construct a probability distribution for the number of operating rooms on any given day.


C. Does it satisfy conditions for valid discrete probability distribution.

Ch. 5


Page 217


#8

A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take one, two, three, or four hours. The different types of malfunctions occur at about the same frequency.




A. Develop a probability distribution for the duration of a service call.


C. Show that your probability distribution satisfies the conditions required for a discrete probability function.


D. What is the probability that a service call will take three hours?


E. A service call has just come in, but the type of malfunction is unknown. It is 3:00 PM and service technicians usually get off work at 5:00 PM. What is the probability that the service technician will have to work overtime to fix the machine today?

Ch. 5


Page 218


#11