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elementary statistics
Elementary Statistics Using Excel Pearson New 5th Edition Mario F Triola - Solutions
Baseball Batting Order If you know the names of the starting batters for a baseball team, what is the probability of randomly selecting a batting order and getting the order that is used in the beginning of the game?
Social Security Numbers A Social Security number consists of nine digits in a particular order, and repetition of digits is allowed. If randomly selecting digits for one Social Security number, what is the probability that you get the Social Security number of the president?
ATM Pin Numbers A thief steals an ATM card and must randomly guess the correct pin code that consists of four digits (0 through 9) that must be entered in the correct order. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
Selections with Replacement When randomly selecting items, if successive selections are made with replacement of previously selected items, which of the five rules of this section apply: (1) fundamental counting rule; (2) factorial rule; (3) permutations rule (when all items are different); (4)
California Daily 4 The winning numbers for the current California Daily 4 lottery are 5, 0, 0, and 4 in that exact order. Because order counts, do calculations for this lottery involve either of the two permutation rules presented in this section? Why or why not? If not, what rule does apply?
California Fantasy The winning numbers for the current California Fantasy 5 lottery are 13, 18, 22, 24, and 32 in any order. Do calculations for winning this lottery involve permutations or combinations? Why?
Notation What does the symbol ! represent? Four different people can stand in a line 4!different ways. What is the actual number of ways that four people can stand in a line?
Confusion of the Inverse In one study, physicians were asked to estimate the probability of a malignant cancer given that a test showed a positive result. They were told that the cancer had a prevalence rate of 1%, the test has a false positive rate of 10%, and the test is 80% accurate in correctly
Unseen Coins A statistics professor tosses two coins that cannot be seen by any students.One student asks this question: “Did one of the coins turn up heads?” Given that the professor’s response is “yes,” find the probability that both coins turned up heads.
Shared Birthdays Find the probability that of 25 randomly selected people,a. no 2 share the same birthday.b. at least 2 share the same birthday.
Composite Water Samples The Fairfield County Department of Public Health tests water for contamination due to the presence of E. coli (Escherichia coli) bacteria. To reduce laboratory costs, water samples from five public swimming areas are combined for one test, and further testing is done only if
Composite Drug Screening Based on the data in Table 1, assume that the probability of a randomly selected person testing positive for drug use is 0.134. If drug screening samples are collected from 8 random subjects and combined, find the probability that the combined sample will reveal a positive
Redundancy in Aircraft Radios The FAA requires that commercial aircraft used for flying in instrument conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.0035. What is the probability that a particular flight will be
Redundancy in Computer Hard Drives Assume that there is a 2% rate of disk drive failure in a year (based on data from various sources, including “Failure Trends in Large Disk Drive Population,” by Pinhero et al. of Google, Inc.).a. If all of your computer data are stored on a hard disk drive
Fraternal Twins If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will give birth to two girls?
Fraternal Twins If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will have one child of each sex?
Fraternal Twinsa. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have fraternal twins?b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twins consisting of one boy and one
Identical Twinsa. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have identical twins?b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twin boys. What is the probability
Negative Predictive Value Find the negative predictive value for the test. That is, find the probability that a subject does not use drugs, given that the test yields a negative result.
Positive Predictive Value Find the positive predictive value for the test. That is, find the probability that a subject uses drugs, given that the test yields a positive result.
Inverse Probabilitiesa. Find P (negative test result subject does not use drugs).b. Find P (subject does not use drugs negative test result).c. Compare the results from parts (a) and (b). Are they equal?
Are P (subject uses drugs negative test result) and P (negative test result subject uses drugs) equal?
Inverse Probabilities Find P (subject uses drugs negative test result). Compare this result to the result found in Exercise
False Negative Find the probability of selecting a subject with a negative test result, given that the subject uses drugs. Who would suffer from this type of error?
False Positive Find the probability of selecting a subject with a positive test result, given that the subject does not use drugs. Why is this particular case problematic for test subjects?
Compliments at Work Based on a poll conducted through e-mail by USA Today, 41%of survey respondents most liked to get compliments at work from their co-workers. Among 12 randomly selected workers, what is the probability of getting at least 1 who most likes to get compliments from co-workers? How
Cleared Burglaries According to FBI data, 12.4% of burglaries are cleared with arrests.A new detective is assigned to five different burglaries.a. What is the probability that at least one of them is cleared with an arrest?b. What is the probability that the detective clears five burglaries with
Car Crashes The probability of a randomly selected car crashing during a year is 0.0423(based on data from the Statistical Abstract of the United States). If a family has three cars, find the probability that at least one of them has a crash during the year. Is there any reason why this probability
Births in China In China, the probability of a baby being a boy is 0.545. Many couples are allowed to have only one child. Among the next five randomly selected births in China, what is the probability that at least one of them is a girl? Can this system continue to work indefinitely?
Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). Among the next five randomly selected births in the United States, what is the probability that at least one of them is a girl?
At Least One Correct Answer If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of getting at least one answer correct, given that the first nine answers are all wrong?
Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having at least one boy after their fifth child is born, given that the first four children were all girls.
At Least One Working Calculator A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates that there is 0.92 probability that the calculator will work on any given day. Because the final exam is so important, she plans to use redundancy by
At Least One Correct Answer If you make random guesses for 10 multiple-choice test questions (each with five possible answers), what is the probability of getting at least 1 correct?If a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you
No 7s When four digits (between 0 and 9 inclusive) are randomly selected with replacement for a lottery ticket, none of the digits is a 7.
At Least One Zero When four digits (between 0 and 9 inclusive) are randomly selected with replacement for a lottery ticket, at least one of the digits is 0.
No Girls When a couple has five children, none of the five is a girl. (Assume that boys and girls are equally likely.)
Five Girls When a couple has five children, all five are girls. (Assume that boys and girls are equally likely.)
Confusion of the Inverse Using the same events A and B described in Exercise 3, what is confusion of the inverse? (Express the answer in both words and symbols.)
Notation Let event A = subject is telling the truth and event B = polygraph test indicates that the subject is lying. Use your own words to translate the notation P1B A2 into a verbal statement.
Conditional Probability What is a conditional probability?
Same Birthdays If 25 people are randomly selected, find the probability that no 2 of them have the same birthday. Ignore leap years.
System Reliability Refer to the figure at the top of the next page in which surge protectors p and q are used to protect an expensive 3D HDTV. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.99 probability of working
Airline Survey Among respondents asked which is their favorite seat on a plane, 492 chose the window seat, 8 chose the middle seat, and 306 chose the aisle seat (based on data from USA Today).a. What is the probability of randomly selecting 1 of the surveyed people and getting one who did not
Online Shopping Survey 427 different adult women were randomly selected and asked what they purchase online, and 162 of the women said that they purchase clothes online(based on a survey by the Consumer Reports Research Center).a. If 2 of the surveyed women are randomly selected without
Flirting In a Microsoft Instant Messaging survey, 1021 adults were asked to identify the most fun way to flirt, and 61of them chose e-mail.a. If 1 of the surveyed adults is randomly selected, what is the probability that this person chose something other than e-mail?b. If 40 of the different
Road Rage In a Prince Market Research survey of 2518 motorists, 252 said that they made an obscene gesture in the previous month.a. If 1 of the surveyed motorists is randomly selected, what is the probability that this motorist did not make an obscene gesture in the previous month?b. If 50 of the
Screening for Marijuana Use If 3 of the subjects are randomly selected without replacement, what is the probability that they all had true negative test results? Is such an event unlikely?
Screening for Marijuana Use If 3 of the subjects are randomly selected without replacement, what is the probability that they all had false positive test results? Is such an event unlikely?
Screening for Marijuana Use If 2 of the subjects are randomly selected without replacement, what is the probability that they both had incorrect test results (either false positive or false negative)? Is such an event unlikely?
Screening for Marijuana Use If 2 of the subjects are randomly selected without replacement, what is the probability that they both had correct test results (either true positive or true negative)? Is such an event unlikely?
Hiring Employees Assume that Google, Inc. hires employees on the different business days of the week (Monday through Friday) with equal likelihood.a. If two different employees are randomly selected, what is the probability that they were both hired on a Monday?b. If two different employees are
Born on the 4th of July For the following, ignore leap years and assume that births on the 365 different days of the year are equally likely.a. What is the probability that a randomly selected person was born on July 4?b. What is the probability that two randomly selected people were both born on
Redundancy in Aircraft Radios The FAA requires that commercial aircraft used for flying in instrument conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.0035. What is the probability that a particular flight will be
Redundancy in Computer Hard Drives It is generally recognized that it is wise to back up computer data. Assume that there is a 2% rate of disk drive failure in a year (based on data from various sources, including “Failure Trends in Large Disk Drive Population,” by Pinhero et al. of Google,
Acceptance Sampling With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. Among 810 airport baggage scales, 102 are defective (based on data from the New York City
Acceptance Sampling With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware,
Pre-Employment Drug Screening If 4 of the 1000 test subjects are randomly selected, find the probability that they all had true negative test results. Is such an event unlikely?a. Assume that the 4 selections are made with replacement.b. Assume that the 4 selections are made without replacement.
Pre-Employment Drug Screening If 3 of the 1000 test subjects are randomly selected, find the probability that they all had correct test results (either true positive or true negative).Is such an event unlikely?a. Assume that the 3 selections are made with replacement.b. Assume that the 3 selections
Pre-Employment Drug Screening If 3 of the 1000 test subjects are randomly selected, find the probability that they all had false negative results. Is it unlikely to randomly select 3 subjects and get 3 results that are all false negative results?a. Assume that the 3 selections are made with
Pre-Employment Drug Screening If 2 of the 1000 test subjects are randomly selected, find the probability that they both had false positive results. Is it unlikely to randomly select 2 subjects and get 2 results that are both false positive results?a. Assume that the 2 selections are made with
A: When an M&M is randomly selected from the 100 M&Ms listed in Data Set 20 in Appendix: Data Sets, it is one of the 8 yellow M&Ms.B: When a second different M&M is randomly selected from those listed in Data Set 20 in Appendix: Data Sets, it is also a yellow M&M.
A: When a survey subject is randomly selected from the 100 senators in the 111th Congress, it is one of the 58 Democrats.B: When a second different senator is randomly selected, it is the one senator who is an Independent.
A: When the first digit (0 through 9) of a four-digit lottery number is chosen by someone buying a ticket, it is the same first digit that is later drawn in the official lottery.B: When the second digit of a four-digit lottery number is chosen by someone buying a ticket, it is the same second digit
A: When one of the 222 coins listed in Data Set 21 in Appendix: Data Sets is randomly selected, it is one of the 5 Indian pennies.B: When another one of the 222 coins listed in Data Set 21 in Appendix: Data Sets is randomly selected, it is also one of the 5 Indian pennies.
A: When a day of the week is randomly selected, it is a Saturday.B: When a second different day of the week is randomly selected, it is a Monday.
A: When a baby is born, it is a girl.B: When a single die is rolled, the outcome is 6.
A: When a baby is born, it is a girl.B: When a second baby is born into a different family, it is also a girl.
A: When a month is randomly selected and ripped from a calendar and destroyed, it is July.B: When a different month is randomly selected and ripped from a calendar, it is November.
Sample for a Poll There are currently 28,741,346 adults in California, and they are all included in one large numbered list. The Gallup organization uses a computer to randomly select 1068 different numbers between 1 and 28,741,346 and then contacts the corresponding adults for a survey. Are the
Independent and Dependent Events True or false: The event of finding that your car’s radio works and the event of finding that your car’s air conditioner works are independent events because they work separately from each other. Explain.
Independent and Dependent Events Are events R and D from Exercise 1 independent or dependent? Explain.
Notation Let R be the event of randomly selecting a senator and getting a Republican, and let D represent the event of randomly selecting a second different senator and getting a Democrat.Use words to describe what the notation P (D | R) represents.
Complements and the Addition Rulea. Develop a formula for the probability of not getting either A or B on a single trial. That is, find an expression for P1A or B2.b. Develop a formula for the probability of not getting A or not getting B on a single trial.That is, find an expression for P1A or
Extending the Addition Rule Extend the formal addition rule to develop an expression for P(A or B or C ). (Hint: Draw a Venn diagram.)
Exclusive Or The formal addition rule expressed the probability of A or B as follows:P1A or B2 = P1A2 + 1B2 - P1A and B2. The exclusive or means either one or the other events occurs, but not both. Rewrite the expression for P(A or B) assuming that the addition rule uses the exclusive or instead of
Disjoint Events If events A and B are disjoint and events B and C are disjoint, must events A and C be disjoint? Give an example supporting your answer.
Gender Selection When analyzing results from a test of the MicroSort gender-selection technique developed by the Genetics & IVF Institute, a researcher wants to compare the results to those obtained from a coin toss. Assume that boys and girls are equally likely and find P(G or H ), which is the
Screening for Marijuana Use Find the probability of a correct result by finding the probability of a true positive or a true negative. How does this result relate to the result from Exercise 37?
Screening for Marijuana Use Find the probability of a false positive or false negative.What does the result suggest about the test’s accuracy?
Screening for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject actually used marijuana. Do you think that the result reflects the marijuana use rate in the general population?
Screening for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested negative or did not use marijuana.
Screening for Marijuana Use If one of the test subjects is randomly selected, find the probability that the subject tested positive or used marijuana.
Screening for Marijuana Usea. How many subjects are included in the study?b. How many subjects did not use marijuana?c. What is the probability that a randomly selected subject did not use marijuana?
Survey Refusals A market researcher is not interested in refusals or subjects below 22 years of age or over 59.Find the probability that the selected person refused to answer or is below 22 or is older than 59.
Survey Refusals A market researcher is interested in responses, especially from those between the ages of 22 and 39, because they are the people more likely to make purchases. Find the probability that a selected subject responds or is between the ages of 22 and 39.
Survey Refusals What is the probability that the selected person refused to respond or is over 59 years of age?
Survey Refusals What is the probability that the selected person responded or is in the 18–21 age bracket?
Survey Refusals A pharmaceutical company is interested in opinions of the elderly, because they are either receiving Medicare or will receive it soon. What is the probability that the selected subject is someone 60 and over who responded?
Survey Refusals What is the probability that the selected person refused to answer?Does that probability value suggest that refusals are a problem for pollsters? Why or why not?
Which Group Did Worse?a. For the physicians given the bottles labeled with a concentration, find the percentage of wrong dosage calculations; then express it as a probability.b. For the physicians given the bottles labeled with a ratio, find the percentage of wrong dosage calculations; then express
Which Group Did Better?a. For the physicians given the bottles labeled with a concentration, find the percentage of correct dosage calculations, then express it as a probability.b. For the physicians given the bottles labeled with a ratio, find the percentage of correct dosage calculations; then
Wrong Dosage or Ratio If one of the physicians is randomly selected, find the probability of getting one who made a wrong dosage calculation or was given the bottle with a ratio label.
Correct or Concentration If one of the physicians is randomly selected, find the probability of getting one who made a correct dosage calculation or was given the bottle with a concentration label.
Wrong Dosage If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose incorrectly? Is that probability as low as it should be?
Correct Dosage If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose correctly? Is that probability as high as it should be?
Drug Screening If one of the subjects is randomly selected, find the probability that the subject had a negative test result or uses drugs.
Drug Screening If one of the subjects is randomly selected, find the probability that the subject had a negative test result or does not use drugs.
Drug Screening If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or does not use drugs.
Drug Screening If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or a negative test result.
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