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Mathematical Interest Theory 3rd Edition Leslie Jane, James Daniel, Federer Vaaler - Solutions
In a Pew Research Center survey of Internet users, 3732 respondents say that they use social networking sites and 1380 respondents say that they do not use social networking sites. What is the probability that a randomly selected person does not use a social networking site? Does that result
A study of the effect of seatbelt use in head-on passenger car collisions found that drivers using a seatbelt had a 64.1% survival rate, while drivers not using a seatbelt had a 41.5% survival rate. If seatbelts have no effect on survival rate, there is less than a 0.0001 chance of getting these
A study on the enhancing effect of coffee on long-term memory found that 35 participants given 200 mg of caffeine performed better on a memory test 24 hours later compared to the placebo group that received no caffeine. a. There was a probability of 0.049 that the difference between the coffee
A study of 420,095 Danish cell phone users resulted in 135 who developed cancer of the brain or nervous system (based on data from the Journal of the National Cancer Institute). When comparing this sample group to another group of people who did not use cell phones, it was found that there is a
In the Kentucky Pick 4 lottery, you can place a "straight" bet of $1 by selecting the exact order of four digits between 0 and 9 inclusive (with repetition allowed), so the probability of winning is 1/10,000. If the same four numbers are drawn in the same order, you collect $5000, so your net
When the horse California Chrome won the 140th Kentucky Derby, a $2 bet on a California Chrome win resulted in a winning ticket worth $7. a. How much net profit was made from a $2 win bet on California Chrome? b. What were the payoff odds against a California Chrome win? c. Based on preliminary
If two orders are selected, find the probability that they are both from Taco Bell.a. Assume that the selections are made with replacement. Are the events independent?b. Assume that the selections are made without replacement. Are the events independent?Assume that orders are randomly selected from
If two orders are selected, find the probability that both of them are not accurate.a. Assume that the selections are made with replacement. Are the events independent?b. Assume that the selections are made without replacement. Are the events independent?Assume that orders are randomly selected
If two orders are selected, find the probability that they are both accurate. a. Assume that the selections are made with replacement. Are the events independent? b. Assume that the selections are made without replacement. Are the events independent?
If two orders are selected, find the probability that they are both from Burger King. a. Assume that the selections are made with replacement. Are the events independent? b. Assume that the selections are made without replacement. Are the events independent?
a. How many subjects are included in the study? b. How many of the subjects had a true negative result? c. What is the probability that a randomly selected subject had a true negative result? Use the results from the "1-Panel-THC" test for marijuana use, which is provided by the company Drug Test
If one of the test subjects is randomly selected, find the probability that the subject did not use marijuana. Do you think that the result reflects the general population rate of subjects who do not use marijuana?
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 22% of the times when they are needed (based on data from Arshad Mansoor, senior vice president with the Electric Power Research Institute). A hospital
Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from "Pacemaker and ICD Generator Malfunctions," by Maisel et al., Journal of the American Medical Association, Vol. 295, No. 16). If the firmware
The National Oceanic and Atmospheric Administration (NOAA) inspects seafood that is to be consumed. The inspection process involves selecting seafood samples from a larger "lot." Assume a lot contains 2875 seafood containers and 288 of these containers include seafood that does not meet inspection
In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from "Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults with Major Trauma,"
There are 15,524,971 adults in Florida. If The Gallup organization randomly selects 1068 adults without replacement, are the selections independent or dependent? If the selections are dependent, can they be treated as being independent for the purposes of calculations?
Refer to the accompanying figure showing surge protectors p and q used to protect an expensive television. If there is a surge in the voltage, the surge protector reduces it to a safe level. Assume that each surge protector has a 0.985 probability of working correctly when a voltage surge occurs.a.
When the author observed a sobriety checkpoint conducted by the Dutchess County Sheriff Department, he saw that 676 drivers were screened and 6 were arrested for driving while intoxicated. Based on those results, we can estimate that P(I) = 0.00888, where I denotes the event of screening a driver
a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.b. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.c. What do the preceding results suggest?In an
a. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.b. Find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.c. What do the preceding results suggest?In an experiment to
a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.b. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.c. What do the preceding results suggest?In an
a. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters.b. Find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.c. What do the preceding results suggest?In an experiment
Assume that there is a 3% rate of disk drive failures in a year (based on data from various sources including lifehacker.com).a. If all of your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid
Using the same events F and H described in Exercise 3, describe confusion of the inverse.
Current rules for telephone area codes allow the use of digits 2-9 for the first digit, and 0-9 for the second and third digits. How many different area codes are possible with these rules? That same rule applies to the exchange numbers, which are the three digits immediately preceding the last
The Digital Pet Rock Company was recently successfully funded via Kickstarter and must now appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a strategic planning committee with four different members. There are
You want to obtain cash by using an ATM, but it's dark and you can't see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.a. What is the probability of selecting a random position and inserting
In the Oregon Pick 4 lottery game, a bettor selects four numbers between 0 and 9 and any selected number can be used more than once. Winning the top prize requires that the selected numbers match those and are drawn in the same order. Do calculations for this lottery involve the combinations rule
The International Morse code is a way of transmitting coded text by using sequences of on>off tones. Each character is 1 or 2 or 3 or 4 or 5 segments long, and each segment is either a dot or a dash. For example, the letter G is transmitted as two dashes followed by a dot, as in - - • . How
a. Five "mathletes" celebrate after solving a particularly challenging problem during competition. If each mathlete high fives each other mathlete exactly once, what is the total number of high fives?b. If n mathletes shake hands with each other exactly once, what is the total number of
About 75% of the U.S. population uses some type of vision correction (such as glasses or contact lenses).a. If someone is randomly selected, what is the probability that he or she does not use vision correction?b. If four different people are randomly selected, what is the probability that they all
a. If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in Japan. Ignore leap years.b. If a person is randomly selected, find the probability that his or her birthday is in October.Ignore leap years.c. Estimate a subjective
The Wild Card lottery is run in the states of Idaho, Montana, North Dakota, and South Dakota. You must select five different numbers between 1 and 33, then you must select one of the picture cards (Ace, King, Queen, Jack), and then you must select one of the four suits (club, heart, diamond,
If A represents the event of randomly selecting one driver included in the table and getting someone who was not killed, what does A̅ represent? Find the value of P(A̅).
Listed below are the blood alcohol concentrations (g/dL) of drivers convicted of drunk driving in fatal car crashes (based on data from the National Highway Traffic Safety Administration).0.09 0.11 0.11 0.13 0.14 0.15 0.17 0.17 0.18 0.18 0.23 0.35Find the value of the following statistics and
Use the same data given in Exercise 1.a. Identify the 5-number summary and also identify any values that appear to be outliers.b. Construct a boxplot.c. Construct a stemplot.
In the Monopoly Millionaires' Club lottery game, you pay $5 and select five different numbers between 1 and 52, and then a sixth number between 1 and 28 is randomly assigned to you. Winning requires that your five numbers match those drawn (in any order), and then your sixth assigned number must
The accompanying table lists probabilities for the corresponding numbers of girls in four births. What is the random variable, what are its possible values, and are its values numerical?
A sociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person (based on a Microsoft Instant Messaging survey). x
Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a self-driving vehicle (based on a TE Connectivity survey). x
When betting on the pass line in the dice game of craps at the Mohegan Sun casino in Connecticut, the table lists the probabilities for the number of bets that must be placed in order to have a win. x
Find the mean and standard deviation for the numbers of girls in 8 births. Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Number of Girls
Use the range rule of thumb to determine whether 1 girl in 8 births is a significantly low number of girls. Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8
Use the range rule of thumb to determine whether 6 girls in 8 births is a significantly high number of girls. Refer to the accompanying table, which describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8
a. Find the probability of getting exactly 7 girls in 8 births. b. Find the probability of getting 7 or more girls in 8 births. c. Which probability is relevant for determining whether 7 is a significantly high number of girls in 10 births: the result from part (a) or part (b)? d. Is 7 a
a. Find the probability of getting exactly 6 girls in 8 births. b. Find the probability of getting 6 or more girls in 8 births. c. Which probability is relevant for determining whether 6 is a significantly high number of girls in 8 births: the result from part (a) or part (b)? d. Is 6 a
a. Find the probability of getting exactly 1 girl in 8 births. b. Find the probability of getting 1 or fewer girls in 8 births. c. Which probability is relevant for determining whether 1 is a significantly low number of girls in 8 births: the result from part (a) or part (b)? d. Is 1 a
Find the mean and standard deviation for the numbers of sleepwalkers in groups of five. Refer to the accompanying table, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from "Prevalence and Comorbidity of Nocturnal Wandering In the U.S. Adult General
Use the range rule of thumb to determine whether 4 is a significantly high number of sleepwalkers in a group of 5 adults. Refer to the accompanying table, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from "Prevalence and Comorbidity of Nocturnal
Use the range rule of thumb to determine whether 3 is a significantly high number of sleepwalkers in a group of 5 adults. Refer to the accompanying table, which describes the numbers of adults in groups of five who reported sleepwalking (based on data from "Prevalence and Comorbidity of Nocturnal
a. Find the probability of getting exactly 4 sleepwalkers among 5 adults. b. Find the probability of getting 4 or more sleepwalkers among 5 adults. c. Which probability is relevant for determining whether 4 is a significantly high number of sleepwalkers among 5 adults: the result from part (a) or
a. Find the probability of getting exactly 1 sleepwalker among 5 adults. b. Find the probability of getting 1 or fewer sleepwalkers among 5 adults. c. Which probability is relevant for determining whether 1 is a significantly low number of sleepwalkers among 5 adults: the result from part (a) or
In the Ohio Pick 4 lottery, you can bet $1 by selecting four digits, each between 0 and 9 inclusive. If the same four numbers are drawn in the same order, you win and collect $5000. a. How many different selections are possible? b. What is the probability of winning? c. If you win, what is your net
In Virginia's Pick 3 lottery game, you can pay $1 to select a three-digit number from 000 through 999. If you select the same sequence of three digits that are drawn, you win and collect $500. a. How many different selections are possible? b. What is the probability of winning? c. If you win, what
There is a 0.9986 probability that a randomly selected 30-year-old male lives through the year (based on data from the U.S. Department of Health and Human Services). A Fidelity life insurance company charges $161 for insuring that the male will live through the year. If the male does not survive
For the accompanying table, is the sum of the values of P(x) equal to 1, as required for a probability distribution? Does the table describe a probability distribution?
There is a 0.9968 probability that a randomly selected 50-year-old female lives through the year (based on data from the U.S. Department of Health and Human Services). A Fidelity life insurance company charges $226 for insuring that the female will live through the year. If she does not survive the
For 100 births, P(exactly 56 girls) = 0.0390 and P(56 or more girls) = 0.136. Is 56 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?
Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. x
Based on a Pitney Bowes survey, assume that 42% of consumers are comfortable having drones deliver their purchases. Suppose we want to find the probability that when five consumers are randomly selected, exactly two of them are comfortable with the drones. What is wrong with using the
Ten different senators from the 113th Congress are randomly selected without replacement, and the numbers of terms that they have served are recorded. Determine whether the given procedure results in a binomial distribution (or a distribution that can be treated as binomial). For those that are not
In an AARP Bulletin survey, 1019 different adults were randomly selected without replacement. Respondents were asked if they have one or more credit cards, and responses were recorded as "yes" and "no." Determine whether the given procedure results in a binomial distribution (or a distribution that
In a survey sponsored by TGI Friday's, 1000 different adult respondents were randomly selected without replacement, and each was asked if they investigate dates on social media before meeting them. Responses consist of "yes" or "no." Determine whether the given procedure results in a binomial
Standard tests, such as the SAT, ACT, or Medical College Admission Test (MCAT), typically use multiple choice questions, each with five possible answers (a, b, c, d, e), one of which is correct. Assume that you guess the answers to the first three questions. a. Use the multiplication rule to find
Based on data from a Harris Interactive survey, 40% of adults say that they prefer to get their news online. Four adults are randomly selected. a. Use the multiplication rule to find the probability that the first three prefer to get their news online and the fourth prefers a different source. That
In the classic legal case of Whitus v. Georgia, a jury pool of 90 people was supposed to be randomly selected from a population in which 27% were minorities. Among the 90 people selected, 7 were minorities. Find the probability of getting 7 or fewer minorities if the jury pool was randomly
A survey sponsored by the Vision Council showed that 79% of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 20 adults are randomly selected, find the probability that at least 19 of them need correction for their eyesight. Is 19 a significantly high number of
Assume that the groups consist of 36 couples. a. Find the mean and standard deviation for the numbers of girls in groups of 36 births. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is the result of 26 girls a result that is
Based on a Pitney Bowes survey, when 1009 consumers were asked if they are comfortable with drones delivering their purchases, 42% said yes. Consider the probability that among 30 different consumers randomly selected from the 1009 who were surveyed, there are at least 10 who are comfortable with
Assume that the groups consist of 16 couples. a. Find the mean and standard deviation for the numbers of girls in groups of 16 births. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is the result of 11 girls a result that is
Assume that offspring peas are randomly selected in groups of 10. a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 10. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is the
Assume that offspring peas are randomly selected in groups of 16. a. Find the mean and standard deviation for the numbers of peas with green pods in the groups of 16. b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high. c. Is a
AAA batteries are made by companies including Duracell, Energizer, Eveready, and Panasonic. When purchasing bulk orders of AAA batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select 50 batteries and determine whether each is within specifications. The entire shipment is
Data Set 27 "M&M Weights" in Appendix B includes data from 100 M&M candies, and 19 of them are green. Mars, Inc. claims that 16% of its plain M&M candies are green. For the following, assume that the claim of 16% is true, and assume that a sample consists of 100 M&Ms. a. Use the range rule of thumb
The County Clerk in Essex, New Jersey, was accused of cheating by not using randomness in assigning line positions on voting ballots. Among 41 different ballots, Democrats were assigned the top line 40 times. Assume that Democrats and Republicans are assigned the top line using a method of random
In a presidential election, 611 randomly selected voters were surveyed, and 308 of them said that they voted for the winning candidate (based on data from ICR Survey Research Group). The actual percentage of votes for the winning candidate was 43%. Assume that 43% of voters actually did vote for
Using the same survey from Exercise 3, the probability of randomly selecting 30 of the 1009 consumers and getting exactly 24 who are comfortable with the drones is represented as 0+. What does 0+ indicate? Does 0+ indicate that it is impossible to get exactly 24 consumers who are comfortable with
One of Mendel's famous experiments with peas resulted in 580 offspring, and 152 of them were yellow peas. Mendel claimed that under the same conditions, 25% of offspring peas would be yellow. Assume that Mendel's claim of 25% is true, and assume that a sample consists of 580 offspring peas. a. Use
The Senate members of the 113th Congress include 80 males and 20 females. Forty different senators are randomly selected without replacement, and the gender of each selected senator is recorded. Determine whether the given procedure results in a binomial distribution (or a distribution that can be
In a recent year, there were 333 murders in New York City. Find the mean number of murders per day, then use that result to find the probability that in a day, there are no murders. Does it appear that there are expected to be many days with no murders?
In Exercise 1 "Notation" we noted that in analyzing hits by V-1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions. a. Find the probability that a randomly selected region had exactly 2
Neuroblastoma, a rare form of cancer, occurs in 11 children in a million, so its probability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12,429 children. a. Assuming that neuroblastoma occurs as usual, find the mean number of cases in groups of 12,429
The recent rate of car fatalities was 33,561 fatalities for 2969 billion miles traveled (based on data from the National Highway Traffic Safety Administration). Find the probability that for the next billion miles traveled, there will be at least one fatality. What does the result indicate about
There is a 1 / 292,201,338 probability of winning the Powerball lottery jackpot with a single ticket. Assume that you purchase a ticket in each of the next 5200 different Powerball games that are run over the next 50 years. Find the probability of winning the jackpot with at least one of those
a. Find the probability that in a year, there will be 5 hurricanes. b. In a 55-year period, how many years are expected to have 5 hurricanes? c. How does the result from part (b) compare to the recent period of 55 years in which 8 years had 5 hurricanes? Does the Poisson distribution work well
a. Find the probability that in a year, there will be no hurricanes. b. In a 55-year period, how many years are expected to have no hurricanes? c. How does the result from part (b) compare to the recent period of 55 years in which there were no years without any hurricanes? Does the Poisson
a. Find the probability that in a year, there will be 7 hurricanes. b. In a 55-year period, how many years are expected to have 7 hurricanes? c. How does the result from part (b) compare to the recent period of 55 years in which 7 years had 7 hurricanes? Does the Poisson distribution work well
a. Find the probability that in a year, there will be 4 hurricanes. b. In a 55-year period, how many years are expected to have 4 hurricanes? c. How does the result from part (b) compare to the recent period of 55 years in which 10 years had 4 hurricanes? Does the Poisson distribution work well
In a recent year, NYU-Langone Medical Center had 4221 births. Find the mean number of births per day, then use that result to find the probability that in a day, there are 15 births. Does it appear likely that on any given day, there will be exactly 15 births?
Currently, an average of 7 residents of the village of Westport (population 760) die each year (based on data from the U.S. National Center for Health Statistics). a. Find the mean number of deaths per day. b. Find the probability that on a given day, there are no deaths. c. Find the probability
Find the probability that at least one of the five adults has a credit card. Does the result apply to five adult friends who are vacationing together? Why or why not?
If all five of the adults have credit cards, is five significantly high? Why or why not?
If the group of five adults includes exactly 1 with a credit card, is that value of 1 significantly low?
In a study of brand recognition of Sony, groups of four consumers are Not Sure 0.30 interviewed. If x is the number of people in the group who recognize the Sony brand name, then x can be 0, 1, 2, 3, or 4, and the corresponding probabilities are 0.0016, 0.0250, 0.1432, 0.3892, and 0.4096. Does the
The Brooklyn District Attorney's office analyzed the leading (leftmost) digits of check amounts in order to identify fraud. The leading digit of 1 is expected to occur 30.1% of the time, according to "Benford's law," which applies in this case. Among 784 checks issued by a suspect company, there
The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant. 0 0 1 2 17 28 21 8 a. Find the mean. b. Find the median. c. Find the
In South Carolina's Pick 3 lottery game, you can pay $1 to select a sequence of three digits, such as 227. If you buy only one ticket and win, your prize is $500 and your net gain is $499. a. If you buy one ticket, what is the probability of winning? b. If you play this game once every day, find
The Society for Human Resource Management conducted a survey of 347 human resource professionals and found that 73% of them reported that their companies do criminal background checks of all job applicants. a. Find the number of respondents who reported that their companies do criminal background
Fox News broadcast a graph similar to the one shown here. The graph is intended to compare the number of people actually enrolled in a government health plan (left bar) and the goal for the number of enrollees (right bar). Does the graph depict the data correctly or is it somehow misleading?
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