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mathematics
elementary statistics picturing

Elementary Statistics 11th Edition Mario F. Triola - Solutions

a. Develop a simulation for finding the probability that when 50 people are randomly selected, at least 2 of them have the same birth date. Describe the simulation and estimate the probability.b. Develop a simulation for finding the probability that when 50 people are randomly selected, at least 3
If four of the test subjects are randomly selected without replacement, find the probability that, in each case, the polygraph indicated that the subject lied. Is such an event unusual?
The probability of randomly selecting an adult who recognizes the brand name of McDonald’s is 0.95 (based on data from Franchise Advantage). Describe a procedure for using software or a TI-83/84 Plus calculator to simulate the random selection of 50 adult consumers. Each individual outcome should
Refer to Data Set 13 in Appendix B. Compare the means and medians from the three different sets of measured voltage levels. Refer to the indicated data set in Appendix B. Use computer software or a calculator to find the means and medians. Data Set 13: Voltage Measurements From a Home All
Listed below are the numbers of bankruptcy filings in Dutchess County, New York State. The numbers are listed in order for each month of a recent year (based on data from the Poughkeepsie Journal ). Is there a trend in the data? If so, how might it be explained?59 85 98 106 120 117 97 95 143 371 14
Find the IQ score separating the top 37% from the others.Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
A genetics experiment involves a population of fruit flies consisting of 1 male named Mike and 3 females named Anna, Barbara, and Chris. Assume that two fruit flies are randomly selected with replacement.a. After listing the 16 different possible samples, find the proportion of females in each
Testing a claim about the mean weight of M&Ms: Right-tailed test with n = 25 and test statistic t = 0.430. Either use technology to find the P-value or use Table A-3 to find a range of values for the P-value. TABLE A-3 t Distribution: Critical t Values Area in One Tail 0.025 Degrees of Freedom
A simple random sample of 40 men results in a standard deviation of 11.3 beats per minute (based on Data Set 1 in Appendix B). The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a
A simple random sample of 32 cars yields a mean weight of 3605.3 lb, a standard deviation of 501.7 lb, and the sample weights appear to be from a normally distributed population (based on Data Set 16 in Appendix B). Use a 0.01 significance level to test the claim that the standard deviation of the
Listed below is a simple random sample of sitting eye heights (in mm) of men (based on anthropometric survey data from Gordon, Churchill, Clauser). Determine whether these sample heights appear to come from a population with a normal distribution. Explain.773 771 821 815 765 811 764 761 778 838 801
Find the critical values and that correspond to the given confidence level X2L and X2R sample size.95%; n = 9
Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 4.8.a. If one ACT score is randomly selected, find the probability that it is greater than 20.0.b. If 25 ACT scores are randomly selected, find the probability that they have a mean greater than 20.c.
Find the critical value zα/2 that corresponds to a 98% confidence level.Find the indicated critical value zα/2.
Mars, Inc., claims that 24% of its M&M plain candies are blue. A sample of 100 M&Ms is randomly selected.a. Find the mean and standard deviation for the numbers of blue M&Ms in such groups of 100.b. Data Set 18 in Appendix B consists of a random sample of 100 M&Ms in which 27 are
Researchers conducted a study to determine whether there were significant differences in graduation rates between medical students admitted through special programs (such as affirmative action) and medical students admitted through the regular admissions criteria. It was found that the graduation
The author purchased a slot machine configured so that there is a 1/2000 probability of winning the jackpot on any individual trial. Although no one would seriously consider tricking the author, suppose that a guest claims that she played the slot machine 5 times and hit the jackpot twice.a. Find
A day bed is 75 in. long.a. Find the percentage of men with heights that exceed the length of a day bed.b. Find the percentage of women with heights that exceed the length of a day bed.c. Based on the preceding results, comment on the length of a day bed.
Find the first quartile Q1, which is the IQ score separating the bottom 25% from the top 75%.Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
DNA (deoxyribonucleic acid) is made of nucleotides. Each nucleotide can contain any one of these nitrogenous bases: A (adenine), G (guanine), C (cytosine), T (thymine). If one of those four bases (A, G, C, T) must be selected three times to form a linear triplet, how many different triplets are
Refer to Table 4-1 (included with the Chapter Problem) and assume that 1 of the 98 test subjects is randomly selected. Find the probability of selecting a subject with a positive test result, given that the subject did not lie. Why is this particular case problematic for test subjects? Table 4-1
People with blood that is group O and type Rh are considered to be universal donors, because they can give blood to anyone. If 4 of the 100 subjects are randomly selected, find the probability that they are all universal donors. a. Assume that the selections are made with replacement. b. Assume
The Bureau of Fisheries once asked for help in finding the shortest route for getting samples from locations in the Gulf of Mexico. How many routes are possible if samples must be taken at 6 locations from a list of 20 locations?
A classical probability problem involves a king who wanted to increase the proportion of women by decreeing that after a mother gives birth to a son, she is prohibited from having any more children. The king reasons that some families will have just one boy, whereas other families will have a few
According to FBI data, 24.9% of robberies are cleared with arrests. A new detective is assigned to 10 different robberies.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 all 10 robberies with arrests?c. What should
If 3 of the 100 subjects are randomly selected, find the probability that they are all group B and type Rh . a. Assume that the selections are made with replacement. b. Assume that the selections are made without replacement. Use the data in the following table, which summarizes blood groups and
Refer to the sample data in Table 4-1. a. How many responses were actually lies? b. If one of the responses is randomly selected, what is the probability that it is a lie? (Express the answer as a fraction.) c. Use the rounding method described in this section to express the answer from part (b)
Based on data from the U.S. Center for Health Statistics, the death rate for males in the 15–24 age bracket is 114.4 per 100,000 population, and the death rate for females in that same age bracket is 44.0 per 100,000 population.a. If a male in that age bracket is randomly selected, what is the
If 2 of the 100 subjects are randomly selected, find the probability that they are both group O and type Rh . a. Assume that the selections are made with replacement. b. Assume that the selections are made without replacement. Use the data in the following table, which summarizes blood groups and
When considering events resulting from a single trial, if one event is the complement of another event, must those two events be disjoint? Why or why not?
Refer to the sample data in Table 4-1, which is included with the Chapter Problem. a. How many responses are summarized in the table? b. How many times did the polygraph provide a negative test result? c. If one of the responses is randomly selected, find the probability that it is a negative test
A pollster for the Gosset Survey Company claims that 30 voters were randomly selected from a population of 2,800,000 eligible voters in New York City (85% of whom are Democrats), and all 30 were Democrats. The pollster claims that this could easily happen by chance. Find the probability of getting
Identity theft often begins by someone discovering your nine-digit social security number or your credit card number. Answer each of the following. Express probabilities as fractions.a. What is the probability of randomly generating nine digits and getting your social security number.b. In the
Answer each of the following.a. Find the probability of selecting the five winning numbers from 1, 2, ... , 31.b. The Wisconsin Badger 5 lottery is won by selecting the correct five numbers from 1, 2, ... , 31. What is the probability of winning if the rules are changed so that in addition to
A problem that once attracted much attention is the Monty Hall problem, based on the old television game show Let’s Make a Deal, hosted by Monty Hall. Suppose you are a contestant who has selected one of three doors after being told that two of them conceal nothing, but that a new red Corvette is
In China, the probability of a baby being a boy is 0.5845. Couples are allowed to have only one child. If relatives give birth to five babies, what is the probability that there is at least one girl? Can that system continue to work indefinitely?
In Example 4 we noted that a study involved equally likely genotypes represented as AA, Aa, aA, and aa. If one of these genotypes is randomly selected as in Example 4, what is the probability that the outcome is AA? Is obtaining AA unusual?
If four of the test subjects are randomly selected without replacement, find the probability that they all had incorrect test results (either false positive or false negative). Is such an event likely?
Nasonex is a nasal spray used to treat allergies. In clinical trials, 1671 subjects were given a placebo, and 2 of them developed upper respiratory tract infections. Another 2103 patients were treated with Nasonex and 6 of them developed upper respiratory tract infections. Assume that Nasonex has
The probability of a randomly selected car crashing during a year is 0.0480 (based on data from the Statistical Abstract of the United States). If a family has four cars, find the probability that at least one of them has a car crash during the year. Is there any reason why the probability might be
A Pew Research Center poll showed that 79% of Americans believe that it is morally wrong to not report all income on tax returns. What is the probability that an American does not have that belief?
Refer to the list of the eight outcomes that are possible when a couple has three children. (See Example 7.) Find the probability of each event.a. There is exactly one girl.b. There are exactly two girls.c. All are girls.
Select the five winning numbers from 1, 2, ... , 36.Find the probability of winning the indicated lottery by buying one ticket. In each case, numbers selected are different and order does not matter. Express the result as a fraction.
As of this writing, the latest results available from the Microsort YSORT method of gender selection consist of 127 boys in 152 births. That is, among 152 sets of parents using the YSORT method for increasing the likelihood of a boy, 127 actually had boys and the other 25 had girls. Assuming that
The FICO (Fair Isaac & Company) score is commonly used as a credit rating. There is a 1% delinquency rate among consumers who have a FICO score above 800. If four consumers with FICO scores above 800 are randomly selected, find the probability that at least one of them becomes delinquent.
If 3 of the 98 test subjects are randomly selected without replacement, find the probability that they all had false positive results. Is it unusual to randomly select 3 subjects without replacement and get 3 results that are all false positive results? Explain.
a. What is the probability of an event that is certain to occur?b. What is the probability of an impossible event?c. A sample space consists of 10 separate events that are equally likely. What is the probability of each?d. On a true/false test, what is the probability of answering a question
Women have a 0.25% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
Use a simulation approach to find the probability that when six consecutive babies are born, there is a run of at least four babies of the same sex. Describe the simulation procedure used, and determine whether such runs are unusual.
Select the six winning numbers from 1, 2, ... , 53.Find the probability of winning the indicated lottery by buying one ticket. In each case, numbers selected are different and order does not matter. Express the result as a fraction.
Based on a recent survey of STATDISK users, it is found that P(M) = 0.05, where M is the event of getting a Macintosh user when a STATDISK user is randomly selected. If a STATDISK user is randomly selected, what does P(M̅) signify? What is its value?
Find the probability of a couple having a baby girl when their fourth child is born, given that the first three children were all girls. Is the result the same as the probability of getting four girls among four children?
If 2 of the 98 test subjects are randomly selected without replacement, find the probability that they both had false positive results. Is it unusual to randomly select 2 subjects without replacement and get 2 results that are both false positive results? Explain.
Which of the following values cannot be probabilities?3:1 2/5 5/2 -0.5 0.5 123/321 321/123 0 1
Use a simulation approach to find the probability that when five consecutive babies are born, there is a run of at least three babies of the same sex. Describe the simulation procedure used, and determine whether such runs are unusual.
Select the six winning numbers from 1, 2, ... , 54.Find the probability of winning the indicated lottery by buying one ticket. In each case, numbers selected are different and order does not matter. Express the result as a fraction.
A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates that there is a 0.96 probability that the calculator will work on any given day. Because the final exam is so important, she plans to use redundancy by bringing in two TI-84 Plus
Randomly selecting a consumer who owns a computerRandomly selecting a consumer who uses the InternetFor each given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5%
When randomly selecting a day of the week, you are certain to select a day containing the letter y.
Randomly selecting a college graduateRandomly selecting someone who is homelessDetermine whether the two events are disjoint for a single trial.
Refer to Exercise 8, which required a description of a hybridization simulation.a. Conduct the simulation and record the number of yellow peas. If possible, obtain a printed copy of the results. Is the percentage of yellow peas from the simulation reasonably close to the value of 25%?b. Repeat the
Refer to Exercise 3. Find the number of different possible trifecta bets in a race with ten horses by evaluating 10P3.Evaluate the given expressions and express all results using the usual format for writing numbers (instead of scientific notation).
If you make guesses for four multiple-choice test questions (each with five possible answers), what is the probability of getting at least one correct? If a very lenient instructor says that passing the test occurs if there is at least one correct answer, can you reasonably expect to pass by
Randomly selecting a consumer from CaliforniaRandomly selecting a consumer who owns a televisionFor each given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline,
Randomly selecting a movie with a rating of RRandomly selecting a movie with a rating of four starsDetermine whether the two events are disjoint for a single trial.
It is impossible to get five aces when selecting cards from a shuffled deck.
The Virginia Win for Life lottery game requires that you select the correct 6 numbers between 1 and 42. Find the number of possible combinations by evaluating 42C6.Evaluate the given expressions and express all results using the usual format for writing numbers (instead of scientific notation).
Refer to Exercise 7, which required a description of a simulated free throw by basketball player Shaquille O’Neal.a. Repeat the simulation five times and record the number of times that the free throw was made. Is the percentage of successful free throws from the simulation reasonably close to
If a couple plans to have 8 children (it could happen), what is the probability that there will be at least one girl? If the couple eventually has 8 children and they are all boys, what can the couple conclude?
Randomly selecting someone treated with the cholesterol-reducing drug LipitorRandomly selecting someone in a control group given no medicationDetermine whether the two events are disjoint for a single trial.
When playing roulette in the Mirage Casino, you have 18 chances out of 38 of winning if you bet that the outcome is an odd number.
Refer to Exercise 6, which required a description of a simulation.a. Conduct the simulation and record the number of left-handed people. Is the percentage of left-handed people from the simulation reasonably close to the value of 10%?b. Repeat the simulation until it has been conducted a total of
A political strategist must visit state capitols, but she has time to visit only 3 of them. Find the number of different possible routes by evaluating 50P3.Evaluate the given expressions and express all results using the usual format for writing numbers (instead of scientific notation).
If a couple plans to have six children, what is the probability that they will have at least one girl? Is that probability high enough for the couple to be very confident that they will get at least one girl in six children?
Finding that your television worksFinding that your refrigerator worksFor each given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be
Receiving a phone call from a volunteer survey subject who believes that there is solid evidence of global warmingReceiving a phone call from a volunteer survey subject who is opposed to stem cell researchDetermine whether the two events are disjoint for a single trial.
When Mendel conducted his famous hybridization experiments, he used peas with green pods and yellow pods. One experiment involved crossing peas in such a way that 75% of the offspring peas were expected to have green pods, and 25% of the offspring peas were expected to have yellow pods. Describe a
When playing roulette at the Bellagio casino in Las Vegas, a gambler is trying to decide whether to bet $5 on the number 13 or to bet $5 that the outcome is any one of these five possibilities: 0 or 00 or 1 or 2 or 3. From Example 8, we know that the expected value of the $5 bet for a single number
America Online conducted a poll by asking its Internet subscribers if they would like to participate in a Sudoku tournament. Among the 4467 Internet users who chose to respond, 40% said “absolutely.”a. What is the probability of selecting one of the respondents and getting someone who responded
Can the events described in Exercise 3 be treated as independent? Explain.
One student conducted the simulation described in Example 3 and stated that the probability of getting a sequence of six 0s or six 1s is 0.977. What is wrong with that statement?
When rolling two dice at the Venetian Casino in Las Vegas, there are 6 chances in 36 that the outcome is a 7.
A manager must select 5 delivery locations from 9 that are available. Find the number of different possible routes by evaluating 9P5.Evaluate the given expressions and express all results using the usual format for writing numbers (instead of scientific notation).
Refer to Exercise 5, which required a description of a simulation.a. Conduct the simulation and record the number of consumers who recognize the brand name of McDonald’s. If possible, obtain a printed copy of the results. Is the proportion of those who recognize McDonald’s reasonably close to
When Brutus asks five different women for a date, at least one of them accepts.Provide a written description of the complement of the given event.
For each given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)Finding that your cell phone worksFinding that your car starts
Determine whether the two events are disjoint for a single trial.Randomly selecting a fruit fly with red eyesRandomly selecting a fruit fly with sepian (dark brown) eyes
When a baby is born, there is approximately a 50-50 chance that the baby is a girl.
Find the number of different possible five-card poker hands by evaluating 52C5.Evaluate the given expressions and express all results using the usual format for writing numbers (instead of scientific notation).
When four males are tested for a particular X-linked recessive gene, none of them are found to have the gene.Provide a written description of the complement of the given event.
For each given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be independent.)Wearing plaid shorts with black socks and sandalsAsking someone
Randomly selecting a Corvette from the Chevrolet assembly line and getting one that is free of defects Randomly selecting a Corvette from the Chevrolet assembly line and getting one with a dead batteryDetermine whether the two events are disjoint for a single trial.
In the game of blackjack played with one deck, a player is initially dealt two cards. Find the number of different two-card initial hands by evaluating 52C2.Evaluate the given expressions and express all results using the usual format for writing numbers (instead of scientific notation).
Shaquille O’Neal is a professional basketball star who had a reputation for being a poor free throw shooter. As of this writing, he made 5155 of the 9762 free throws that he attempted, for a success ratio of 0.528. Describe a procedure for using software or a TI-83/84 Plus calculator to simulate
When six defibrillators are purchased by the New York University School of Medicine, all of them are free of defects.Provide a written description of the complement of the given event.
Finding that your car radio worksFinding that your car headlights workFor each given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independent according to the 5% guideline, consider them to be
Conducting a Pew Research Center poll and randomly selecting a subject who is a RepublicanConducting a Pew Research Center poll and randomly selecting a subject who is a DemocratDetermine whether the two events are disjoint for a single trial.
A WeatherBug forecast for the author’s home was stated as: “Chance of rain: 80%.”
Find the number of different ways that the nine players on a baseball team can line up for the National Anthem by evaluating 9!.Evaluate the given expressions and express all results using the usual format for writing numbers (instead of scientific notation).
Ten percent of people are left-handed. In a study of dexterity, 15 people are randomly selected. Describe a procedure for using software or a TI-83/84 Plus calculator to simulate the random selection of 15 people. Each of the 15 outcomes should be an indication of one of two results: (1) Subject is

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