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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions
Twenty percent of cars that are inspected have faulty pollution control systems. The cost of repairing a pollution control system exceeds $100 about 40% of the time. When a driver takes her car in for inspection, what's the probability that she will end up paying more than $100 to repair the
You are dealt a hand of three cards, one at a time. Find the probability of each of the following.a) The first heart you get is the third card dealt.b) Your cards are all red (that is, all diamonds or hearts).c) You get no spades.d) You have at least one ace.
What is the probability that a person likes to watch football, given that she also likes to watch basketball?
You pick three cards at random from a deck. Find the probability of each event described below.a) You get no aces.b) You get all hearts.c) The third card is your first red card.d) You have at least one diamond.
A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time and testing them. Find the probability of each outcome.a) The first two you choose are both good.b) At least one of the first three works.c) The first four you pick all
The soccer team's shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of each event described. a) The first two you
A university requires its biology majors to take a course called BioResearch. The prerequisite for this course is that students must have taken either a Statistics course or a computer course. By the time they are juniors, 52% of the Biology majors have taken Statistics, 23% have had a computer
Fifty-six percent of all American workers have a workplace retirement plan, 68% have health insurance, and 49% have both benefits. We select a worker at random. a) What's the probability he has neither employer-sponsored health insurance nor a retirement plan? b) What's the probability he has
A survey found that 73% of Americans have a home phone, 83% have a cell phone and 58% of people have both. a) If a person has a home phone, what's the probability that they have a cell phone also? b) Are having a home phone and a cell phone independent events? Explain. c) Are having a home phone
According to Exercise 16, the probability that a U.S. resident has traveled to Canada is 0.18, to Mexico is 0.09, and to both countries is 0.04. a) What's the probability that someone who has traveled to Mexico has visited Canada too? b) Are traveling to Mexico and to Canada disjoint events?
If you draw a card at random from a well-shuffled deck, is getting an ace independent of the suit? Explain.
The local animal shelter in Exercise 22 reported that it currently has 24 dogs and 18 cats available for adoption; 8 of the dogs and 6 of the cats are male. Are the species and sex of the animals independent? Explain.
Early in 2010, Consumer Reports published the results of an extensive investigation of broiler chickens purchased from food stores in 23 states. Tests for bacteria in the meat showed that 62% of the chickens were contaminated with Campylobacter, 14% with salmonella, and 9% with both. a) What's the
From Exercise 3, if someone doesn't like to watch basketball, what is the probability that she will be a football fan?
In Exercises 20 and 26, we looked at the birth orders and college choices of some Intro Stats students. For these students:a) Are enrolling in Agriculture and Human Ecology disjoint? Explain.b) Are enrolling in Agriculture and Human Ecology independent? Explain.c) Are being firstborn and enrolling
Given the table of probabilities from Exercise 23, are high blood pressure and high cholesterol independent? Explain.
Given the table of probabilities from Exercise 24, are party affiliation and position on immigration independent? Explain.
According to estimates from the federal government's 2010 National Health Interview Survey, based on face-to-face interviews in 16,676 households, approximately 63.6% of U.S. adults have both a landline in their residence and a cell phone, 25.4% have only cell phone service but no landline, and
After surveying 995 adults, 81.5% of whom were over 30, the National Sleep Foundation reported that 36.8% of all the adults snored. 32% of the respondents were snorers over the age of 30. a) What percent of the respondents were 30 or less and did not snore? b) Is snoring independent of age? Explain.
A poll conducted by Gallup classified respondents by sex and political party, as shown in the table.Is party affiliation independent of the respondents' sex? Explain.
A random survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. Is country of origin independent of type of driver?
Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the
A private college report contains these statistics: 70% of incoming freshmen attended public schools. 75% of public school students who enroll as freshmen eventually graduate. 90% of other freshmen eventually graduate. a) Is there any evidence that a freshman's chances to graduate may depend upon
Remember Leah (Exercise 47)? Suppose you pick her up at the Denver airport, and her luggage is not there. What is the probability that Leah's first flight was delayed? Exercise 47 Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is
A student figures that he has a 30% chance of being let out of class late. If he leaves class late, there is a 45% chance that he will miss his train. What is the probability that it will cause him to miss the train?
What percent of students who graduate from the college in Exercise 48 attended a public high school? Exercise 48 A private college report contains these statistics: 70% of incoming freshmen attended public schools. 75% of public school students who enroll as freshmen eventually graduate. 90% of
A company's records indicate that on any given day about 1 % of their day-shift employees and 2% of the night-shift employees will miss work. Sixty percent of the employees work the day shift. a) Is absenteeism independent of shift worked? Explain. b) What percent of employees are absent on any
Pewlnternet reported in January of 2014 that 32% of U.S. adults own at least one e-reader, and that 28% of U.S. adults read at least one e-book in the previous year (and thus, presumably, owned an e-reader). Overall, 76% of U.S. adults read at least one book (electronic or otherwise) in the
At the company described in Exercise 51, what percent of the absent employees are on the night shift? Exercise 51 A company's records indicate that on any given day about 1 % of their day-shift employees and 2% of the night-shift employees will miss work. Sixty percent of the employees work the day
Given the e-reader data presented in Exercise 52. a) If a randomly selected U.S. adult has an e-reader, what is the probability that he or she hasn't read an e-book in the past year? b) Is it more or less likely that a randomly selected U.S. adult who does not own an e-reader would have read no
Police often set up sobriety checkpoints—roadblocks where drivers are asked a few brief questions to allow the officer to judge whether or not the person may have been drinking. If the officer does not suspect a problem, drivers are released to go on their way. Otherwise, drivers are detained for
An airline offers discounted "advance-purchase" fares to customers who buy tickets more than 30 days before travel and charges "regular" fares for tickets purchased during those last 30 days. The company has noticed that 60% of its customers take advantage of the advance-purchase fares. The
Dan's Diner employs three dishwashers. Al washes 40% of the dishes and breaks only 1 % of those he handles. Betty and Chuck each wash 30% of the dishes, and Betty breaks only 1 % of hers, but Chuck breaks 3% of the dishes he washes. (He, of course, will need a new job soon....) You go to Dan's for
A company manufacturing electronic components for home entertainment systems buys electrical connectors from three suppliers. The company prefers to use supplier A because only 1% of those connectors prove to be defective, but supplier A can deliver only 70% of the connectors needed. The company
In July 2005, the journal Annals of Internal Medicine published a report on the reliability of HIV testing. Results of a large study suggested that among people with HIV, 99.7% of tests conducted were (correctly) positive, while for people without HIV 98.5% of the tests were (correctly) negative. A
A nervous kicker usually makes 70% of his first field goal attempts. If he makes his first attempt, his success rate rises to 90%. What is the probability that he makes his first two kicks?
Lie detectors are controversial instruments, barred from use as evidence in many courts. Nonetheless, many employers use lie detector screening as part of their hiring process in the hope that they can avoid hiring people who might be dishonest. There has been some research, but no agreement, about
On the Titanic, the probability of survival was 0.323. Among first class passengers, it was 0.625. Were survival and ticket class independent? Explain.
If the sex of a child is independent of all other births, is the probability of a woman giving birth to a girl after having four boys greater than it was on her first birth? Explain.
Facebook reports that 70% of its users are from outside the United States and that 50% of its users log on to Facebook every day. Suppose that 20% of its users are U.S. users who log on every day. Make a probability table. Why is a table better than a tree here?
A citrus farmer has observed the following distribution for the number of oranges per tree. How many oranges does he expect on average?
Find the expected value of each random variable:a)b)
You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $20 for the ace of clubs. a) Create a probability model for the amount you win. b) Find the expected amount you'll win. c) What would you be willing to pay to
You roll a die. If it comes up a 6, you win $100. If not, you get to roll again. If you get a 6 the second time, you win $50. If not, you lose. a) Create a probability model for the amount you win. b) Find the expected amount you'll win. c) What would you be willing to pay to play this game?
A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.)a) Create a probability model for the number of children they might have.b) Find the expected number of children.c)
A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it. It costs $5 to play, and you're willing to spend up to $20 trying to win. You estimate that you have about a 10% chance of hitting the balloon on any throw. a) Create a probability model for this
A small software company bids on two contracts and knows it can only get one of them. It anticipates a profit of $50,000 if it gets the larger contract and a profit of $20,000 on the smaller contract. The company estimates there's a 30% chance it will get the larger contract and a 60% chance it
A man buys a racehorse for $20,000 and enters it in two races. He plans to sell the horse afterward, hoping to make a profit. If the horse wins both races, its value will jump to $100,000. If it wins one of the races, it will be worth $50,000. If it loses both races, it will be worth only $10,000.
Find the standard deviations of the random variables in Exercise 9.In Exercise 9a)b)
Find the standard deviations of the random variables in Exercise 10.In Exercise 10a)b)
Find the standard deviation of the amount you might win drawing a card in Exercise 11. Exercise 11 You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $20 for the ace of clubs.
A coffee shop tracks sales and has observed the distribution in the following table. What is the average daily sales that it can expect?
Find the standard deviation of the amount you might win rolling a die in Exercise 12. Exercise 12 You roll a die. If it comes up a 6, you win $100. If not, you get to roll again. If you get a 6 the second time, you win $50. If not, you lose.
Find the standard deviation of the number of children the couple in Exercise 13 may have. Exercise 13 A couple plans to have children until they get a girl, but they agree that they will not have more than three children even if all are boys. (Assume boys and girls are equally likely.)
Find the standard deviation of your winnings throwing darts in Exercise 14. Exercise 14 A carnival game offers a $100 cash prize for anyone who can break a balloon by throwing a dart at it. It costs $5 to play, and you're willing to spend up to $20 trying to win. You estimate that you have about a
The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour.a) How many calls should the shop expect per hour?b) What is the standard deviation?
A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.a) How many red lights should she expect to hit each day?b) What's the standard deviation?
A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While none had more than three of these defects, 7% had three, 11% two, and 21% one defect. Find the expected number of appearance defects in a new car and the standard
An insurance policy costs $ 100 and will pay policyholders $10,000 if they suffer a major injury (resulting in hospitalization) or $3000 if they suffer a minor injury (resulting in lost time from work). The company estimates that each year 1 in every 2000 policyholders may have a major injury, and
Mary is deciding whether to book the cheaper flight home from college after her final exams, but she's unsure when her last exam will be. She thinks there is only a 20% chance that the exam will be scheduled after the last day she can get a seat on the cheaper flight. If it is and she has to cancel
An option to buy a stock is priced at $200. If the stock closes above 30 on May 15, the option will be worth $ 1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30 (inclusively), the option will be worth $200. A trader thinks there is a 50% chance that
You play two games against the same opponent. The probability you win the first game is 0.4. If you win the first game, the probability you also win the second is 0.2. If you lose the first game, the probability that you win the second is 0.3. a) Are the two games independent? Explain. b) What's
What is the standard deviation for Exercise 1?
Your company bids for two contracts. You believe the probability you get contract #1 is 0.8. If you get contract #1, the probability you also get contract #2 will be 0.2, and if you do not get #1, the probability you get #2 will be 0.3.a) Are the two contracts independent? Explain.b) Find the
In a group of 10 batteries, 3 are dead. You choose 2 batteries at random. a) Create a probability model for the number of good batteries you get. b) What's the expected number of good ones you get? c) What's the standard deviation?
In a litter of seven kittens, three are female. You pick two kittens at random. a) Create a probability model for the number of male kittens you get. b) What's the expected number of males? c) What's the standard deviation?
Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of:a) 3Xb) Y + 6c) X + Yd) X - Ye) X1 + X2
Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of:a) X - 20b) 0.5Yc) X + Yd) X - Ye) Y1 + Y2
Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of:a) 0.8Yb) 2X - 100c) X + 2Yd) 3X - Ye) Y1 +Y2
Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of:a) 2Y + 20b) 3Xc) 0.25X + Yd) X - 5Ye) X1 + X2 + X3
A grocery supplier believes that in a dozen eggs, the mean number of broken ones is 0.6 with a standard deviation of 0.5 eggs. You buy 3 dozen eggs without checking them. a) How many broken eggs do you expect to get? b) What's the standard deviation? c) What assumptions did you have to make about
A company selling vegetable seeds in packets of 20 estimates that the mean number of seeds that will actually grow is 18, with a standard deviation of 1.2 seeds. You buy 5 different seed packets. a) How many bad (non-growing) seeds do you expect to get? b) What's the standard deviation? c) What
Find the mean and standard deviation of the number of repair calls the appliance shop in Exercise 23 should expect during an 8-hour day.
What is the standard deviation for Exercise 2?
Find the mean and standard deviation of the number of red lights the commuter in Exercise 24 should expect to hit on her way to work during a 5-day work week.
A delivery company's trucks occasionally get parking tickets, and based on past experience, the company plans that each truck will average 1.3 tickets a month, with a standard deviation of 0.7 tickets. a) If they have 18 trucks, what are the mean and standard deviation of the total number of
Organizers of a televised fundraiser know from past experience that most people donate small amounts ($10—$25), some donate larger amounts ($50-$ 100), and a few people make very generous donations of $250, $500, or more. Historically, pledges average about $32 with a standard deviation of
An insurance company estimates that it should make an annual profit of $ 150 on each homeowner's policy written, with a standard deviation of $6000. a) Why is the standard deviation so large? b) If it writes only two of these policies, what are the mean and standard deviation of the annual
A casino knows that people play the slot machines in hopes of hitting the jackpot but that most of them lose their dollar. Suppose a certain machine pays out an average of $0.92, with a standard deviation of $120. a) Why is the standard deviation so large? b) If you play 5 times, what are the mean
The amount of cereal that can be poured into a small bowl varies with a mean of 1.5 ounces and a standard deviation of 0.3 ounces. A large bowl holds a mean of 2.5 ounces with a standard deviation of 0.4 ounces. You open a new box of cereal and pour one large and one small bowl. a) How much more
The American Veterinary Association claims that the annual cost of medical care for dogs averages $ 100, with a standard deviation of $30, and for cats averages $ 120, with a standard deviation of $35. a) What's the expected difference in the cost of medical care for dogs and cats? b) What's the
In Exercise 45 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes is a random variable with mean 16.2 ounces and standard deviation 0.1 ounces. a) Find the expected amount of cereal left in the box. b) What's the standard
You're thinking about getting two dogs and a cat. Assume that annual veterinary expenses are independent and have a Normal model with the means and standard deviations described in Exercise 46. a) Define appropriate variables and express the total annual veterinary costs you may have. b) Describe
In the 4 Ã 100 medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the following assumptions:¢ The swimmers'
An employer pays a mean salary for a 5-day workweek of $ 1250 with a standard deviation of $129. On the weekends, his salary expenses have a mean of $450 with a standard deviation of $57. What is the mean and standard deviation of his total weekly salaries?
Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take:¢ The times for each setup phase are
A farmer has 100 lb of apples and 50 lb of potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of 0.5 dollars and a standard deviation of 0.2 dollars. Similarly, for a pound of potatoes, the mean price is 0.3 dollars and the standard deviation is 0.1
The bicycle shop in Exercise 50 will be offering 2 specially priced children's models at a sidewalk sale. The basic model will sell for $120 and the deluxe model for $150. Past experience indicates that sales of the basic model will have a mean of 5.4 bikes with a standard deviation of 1.2, and
At a certain coffee shop, all the customers buy a cup of coffee; some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 320 cups and a standard deviation of 20 cups. He also believes that the number of doughnuts he sells
The Atlas BodyBuilding Company (ABC) sells "starter sets" of barbells that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pounds. The weights average the specified amounts, but the standard deviations are
A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of 11. Assuming that the second 9 has the same mean and standard deviation, what is the mean and standard deviation of his total score if he plays a full 18
The life span of a calculator battery is normally distributed with a mean of 45 hours and a standard deviation of 5 hours. What is the probability that a battery lasts more than 53 hours?
An automatic filling machine in a factory fills bottles of ketchup with a mean of 16.1 oz and a standard deviation of 0.05 oz with a distribution that can be well modeled by a Normal model. What is the probability that your bottle of ketchup contains less than 16 oz?
Find the expected value of each random variable:a)b)
An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via smartphones so they want to estimate the proportion of users who access the site that way (even if they also use their computers sometimes).
A machine is supposed to fill cans with 16 oz of soup. Of course there, will be some variation in the amount actually dispensed, and measurement errors are often approximately normally distributed. The manager would like to understand the variability of the variances of the samples, so he collects
A marketing researcher for a phone company surveys 100 people and finds that the proportion of customers who are likely to switch providers when their contract expires is 15%. a) What is the standard deviation of the sampling distribution of the proportion? b) If she wants to reduce the standard
A market researcher for a provider of iPod accessories wants to know the proportion of customers who own cars to assess the market for a new iPod car charger. A survey of 500 customers indicates that 76% own cars. a) What is the standard deviation of the sampling distribution of the proportion? b)
A waiter believes the distribution of his tips has a model that is slightly skewed to the right, with a mean of $9.60 and a standard deviation of $5.40. a) Explain why you cannot determine the probability that a given party will tip him at least $20. b) Can you estimate the probability that the
A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of $20. a) Explain why you cannot determine the probability that the next Sunday customer will spend at least $40. b) Can you estimate the probability that the next
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