Question: In Exercise 45 we poured a large

> Worldwide, tuberculosis is the number-one cause of death from an infectious disease. But the majority of cases are in developing countries. In the U.S., the probability of contracting TB is small, with p about 0.0005 for a new case in a given year. In a

> I am the only bank teller on duty at my local bank. I need to run out for 10 minutes, but I don’t want to miss any customers. Suppose the arrival of customers can be modeled by a Poisson distribution with mean 2 customers per hour. 1. What the probabilit

> We have looked at various facts about hurricanes in previous chapters. Suppose we find that the arrivals of hurricanes can be modeled by a Poisson distribution with mean 2.45. 1. What the probability of no hurricanes next year? 2. What the probability th

> Shortly after the introduction of the euro coin in Belgium, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 140 heads that 56% heads. Do you

> A newly hired telemarketer is told he will probably make a sale on about 12% of his phone calls. The first week he called 200 people, but only made 10 sales. Should he suspect he was misled about the true success rate? Explain.

> An airline, believing that 5% of passengers fail to show up for flights, overbooks (sells more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What the probability the airline will not have enou

> A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The average size of classes that meet there is 188, and we can assume that about 13% of students are left-handed. What the probability that a right-handed s

> Based on concerns raised by his preliminary research, the biologist in Exercise 38 decides to collect and examine 150 frogs. 1. Assuming the frequency of the trait is still 1 in 8, determine the mean and standard deviation of the number of frogs with the

> Here are the annual numbers of deaths from floods in the United States from 1995 through 2015: 80, 131, 118, 136, 68, 38, 48, 49, 86, 82, 43, 76, 87, 82, 56, 103, 113, 29, 82, 38, 176 Find these statistics: 1. mean 2. median and quartiles 3. range and IQ

> An orchard owner knows that he’ll have to use about 6% of the apples he harvests for cider because they will have bruises or blemishes. He expects a tree to produce about 300 apples. 1. Describe an appropriate model for the number of cider apples that ma

> The archer in Exercise 30 will be shooting 200 arrows in a large competition. 1. What are the mean and standard deviation of the number of bull-eyes she might get? 2. Is a Normal model appropriate here? Explain. 3. Use the 68 95 99.7 Rule to describe the

> Suppose the tennis player in Exercise 37 serves 80 times in a match. 1. What are the mean and standard deviation of the number of good first serves expected? 2. Verify that you can use a Normal model to approximate the distribution of the number of good

> A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in 1 of every 8 frogs. He collects and examines a

> A certain tennis player makes a successful first serve 70% of the time. Assume that each serve is independent of the others. If she serves 6 times, what the probability she gets 1. all 6 serves in? 2. exactly 4 serves in? 3. at least 4 serves in? 4. no m

> At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many internationa

> It is generally believed that nearsightedness affects about 12% of all children. A school district tests the vision of 169 incoming kindergarten children. How many would you expect to be nearsighted? With what standard deviation?

> Suppose the archer from Exercise 30 shoots 10 arrows. 1. Find the mean and standard deviation of the number of bull-eyes she may get. 2. What the probability that she never misses? 3. What the probability that there are no more than 8 bull-eyes? 4. What

> Suppose we choose 12 people instead of the 5 chosen in Exercise 29 . 1. Find the mean and standard deviation of the number of right-handers in the group. 2. What the probability that they’re not all right-handed? 3. What the probability that there are no

> Consider our archer from Exercise 30 . 1. How many bull-eyes do you expect her to get? 2. With what standard deviation? 3. If she keeps shooting arrows until she hits the bull-eye, how long do you expect it will take?

> Here are the number of domestic flights flown in each year from 2000 to 2016 (www.transtats.bts.gov/homepage.asp): a) Find the correlation of Flights with Year. b) Make a scatterplot and describe the trend. c) Why is the correlation you found in part a n

> Consider our group of 5 people from Exercise 29 . 1. How many lefties do you expect? 2. With what standard deviation? 3. If we keep picking people until we find a lefty, how long do you expect it will take?

> An Olympic archer is able to hit the bull-eye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what the probability of each of the following results? 1. Her first bull-eye comes on the third arrow. 2. She misses the

> Assume that 13% of people are left-handed. If we select 5 people at random, find the probability of each outcome. 1. The first lefty is the fifth person chosen. 2. There are some lefties among the 5 people. 3. The first lefty is the second or third perso

> An American roulette wheel has 38 slots, of which 18 are red, 18 are black, and 2 are green (0 and 00). If you spin the wheel 38 times, 1. Intuitively, how many times would you expect the ball to wind up in a green slot? 2. Use the formula for expected v

> If you flip a fair coin 100 times, 1. Intuitively, how many heads do you expect? 2. Use the formula for expected value to verify your intuition.

> About 8% of males are color-blind. A researcher needs some color-blind subjects for an experiment and begins checking potential subjects. 1. On average, how many men should the researcher expect to check to find one who is color-blind? 2. What the probab

> Only 4% of people have Type AB blood. 1. On average, how many donors must be checked to find someone with Type AB blood? 2. What the probability that there is a Type AB donor among the first 5 people checked? 3. What the probability that the first Type A

> Justine works for an organization committed to raising money for Alzheimer research. From past experience, the organization knows that about 20% of all potential donors will agree to give something if contacted by phone. They also know that of all people

> Raaj works at the customer service call center of a major credit card bank. Cardholders call for a variety of reasons, but regardless of their reason for calling, if they hold a platinum card, Raaj is instructed to offer them a double-miles promotion. Ab

> For the computer chips described in Exercise 20 , how many do you expect to test before finding a bad one?

> On August 24, 2006, the International Astronomical Union voted that Pluto is not a planet. Some members of the public have been reluctant to accept that decision. Let look at some of the data. Is there any pattern to the locations of the planets? The tab

> For the basketball player in Exercise 19 , what the expected number of shots until he misses?

> Suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing. 1. What the probability that the fifth chip you test is the first bad one you find? 2. What the probability you find a bad one within the first 10 yo

> A basketball player has made 80% of his foul shots during the season. Assuming the shots are independent, find the probability that in tonight game he 1. misses for the first time on his fifth attempt. 2. makes his first basket on his fourth shot. 3. mak

> A Department of Transportation report about air travel found that airlines misplace about 5 bags per 1000 passengers. Suppose you are traveling with a group of people who have checked 22 pieces of luggage on your flight. Can you consider the fate of thes

> A Department of Transportation report about air travel found that, nationwide, 76% of all flights are on time. Suppose you are at the airport and your flight is one of 50 scheduled to take off in the next two hours. Can you consider these departures to b

> Suppose 75% of all drivers always wear their seatbelts. Let investigate how many of the drivers might be belted among five cars waiting at a traffic light. 1. Describe how you would simulate the number of seatbelt-wearing drivers among the five cars. 2.

> Let take one last look at the Hope Solo picture search. You know her picture is in 20% of the cereal boxes. You buy five boxes to see how many pictures of Hope you might get. 1. Describe how you would simulate the number of pictures of Hope you might fin

> You are one space short of winning a child board game and must roll a 1 on a die to claim victory. You want to know how many rolls it might take. 1. Describe how you would simulate rolling the die until you get a 1. 2. Run at least 30 trials. 3. Based on

> Think about the Hope Solo picture search again. You are opening boxes of cereal one at a time looking for her picture, which is in 20% of the boxes. You want to know how many boxes you might have to open in order to find Hope. 1. Describe how you would s

> Find the expected value of each random variable:

> The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weight-in-motion scale. To see if the new device was accurate, they conducted a calibrati

> The Atlas Body Building 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 specifi

> 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 beli

> The bicycle shop in Exercise 50 will be offering 2 specially priced children 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 bike

> 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

> 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

> In the 4—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 follow

> 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 . 1. Define appropriate variables and express the total annua

> 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. 1. What the expected difference in the cost of medical

> 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

> For the roller coaster data in Exercise 49: 1. Explain why in looking for a variable that explains rank, you will be hoping for a negative correlation. 2. Do any of the provided variables provide a strong predictor for roller coaster rank?

> 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. 1. Why is the standard deviation so larg

> An insurance company estimates that it should make an annual profit of $150 on each homeowner policy written, with a standard deviation of $6000. 1. Why is the standard deviation so large? 2. If it writes only two of these policies, what are the mean and

> 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 abo

> A delivery company 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. 1. If they have 18 trucks, what are the mean and stand

> 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.

> 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.

> 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. 1. How many bad (non-growing) seeds do you expect to get?

> 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. 1. How many broken eggs do you expect to get? 2. What the standard deviation? 3. Wh

> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 1. 2Y+20 2. 3X 3. 0.25X+Y 4. X5Y 5. X1+X2+X3

> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 1. 0.8Y 2. 2X100 3. X+2Y 4. 3XY 5. Y1+Y2

> For the roller coaster data in Exercise 49: 1. Examine the relationship between Initial Drop and Speed. 2. Examine the relationship between Initial Drop and Height. 3. What conclusions can you safely draw about the initial drop of a roller coaster? Is In

> A random sample of 1000 patients was taken from a large medical center database. The six variables included are Sex (M/F), Age (years), Insurance coverage (yes/no), Number of children (010), Marital status (single, married, divorced, widowed), Number of

> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 1. X20 2. 0.5Y 3. X+Y 4. XY 5. Y1+Y2

> Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: 1. 3X 2. Y+6 3. X+Y 4. XY 5. X1+X2

> In a litter of seven kittens, three are female. You pick two kittens at random. 1. Create a probability model for the number of male kittens you get. 2. What the expected number of males? 3. What the standard deviation?

> In a group of 10 batteries, 3 are dead. You choose 2 batteries at random. 1. Create a probability model for the number of good batteries you get. 2. What the expected number of good ones you get? 3. What the standard deviation?

> 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. 1. Are the two co

> 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. 1. Are the

> 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.

> Mary is deciding whether to book the cheaper flight home from college after her final exams, but she 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 che

> 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

> 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 d

> Since 1994, the Best Roller Coaster Poll (www.ushsho.com/bestrollercoasterpoll.htm) has been ranking the world best roller coasters. In 2013, Bizarro dropped to 4th after earning the top steel coaster rank for six straight years. Data on the top 14 steel

> 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. 1. How many red lights should she expect to hit

> The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. 1. How many calls should the shop expect per hour? 2. What is the standard deviation?

> Find the standard deviation of your winnings throwing darts in Exercise 14 .

> Find the standard deviation of the number of children the couple in Exercise 13 may have.

> Find the standard deviation of the amount you might win rolling a die in Exercise 12 .

> Find the standard deviation of the amount you might win drawing a card in Exercise 11 .

> Find the standard deviations of the random variables in Exercise 10 .

> Find the standard deviations of the random variables in Exercise 9 .

> 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 lose

> 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 a 30% chance it will get

> In a dataset of 1057 New York homes offered for sale, a histogram of the ages looks like this: We drew 1000 samples of 105 homes from this dataset and found the IQR and the range of each sample. Below are histograms of the 1000 IQRs and 1000 ranges. For

> 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 th

> 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.) 1. Create a probability model for the number of children they might h

> 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. 1. Create probability model for the amount you win. 2. Find the expected amount you’ll win. 3. What would you

> 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. 1. Create a probability model for the amount you win. 2. Find the expected amount you’l

> Find the expected value of each random variable:

> A certain company believes that 95% of its job applicants are trustworthy. The company gives everyone a polygraph test, asking, Have you ever stolen anything from your place of work? Naturally, all the applicants answer No, but the polygraph identifies

> 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 ha

> 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

> 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

> Dan 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

> Return to the data on roller coasters seen in Exercise 23. Here is the distribution of the lengths of the rides of 241 coasters. We drew samples of 60 coasters from the full set of 241. We then repeated this 1000 times. For each sample, we found the mean

> 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 o

> Police often set up sobriety check points 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 th

> Given the e-reader data presented in Exercise 52: 1. 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? 2. Is it more or less likely that a randomly selected U.S. adult who do