In an effort to check the quality of their cell phones, a manufacturing manager decides to take a random sample of 10 cell phones from yesterday production run, which produced cell phones with serial numbers ranging (according to when they were produced) from 43005000 to 43005999. If each of the 1000 phones is equally likely to be selected: 1. What distribution would they use to model the selection? 2. What is the probability that a randomly selected cell phone will be one of the last 100 to be produced? 3. What is the probability that the first cell phone selected is either from the last 200 to be produced or from the first 50 to be produced?
> 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. 1. Explain why you cannot determine the probability that a given party will tip him at least $20. 2.
> Based on meteorological data for the past century, a local TV weather forecaster estimates that the region average winter snowfall is 23", with a margin of error of ±2 inches. Assuming he used a 95% confidence interval, how should viewers interpret this
> After surveying students at Dartmouth College, a campus organization calculated that a 95% confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester calendar) is ($1372, $1562). Now the organization is trying to writ
> Here are boxplots of the points scored during the first 10 games of the season for both Scyrine and Alexandra: 1. Summarize the similarities and differences in their performance so far. 2. The coach can take only one player to the state championship. Whi
> A biology class conducts a bird count every week during the semester. Using the number of species counted each week, a student finds the following confidence interval for the mean number of species counted: Knowing that species have to be whole numbers,
> The LSAT (a test taken for law school admission) has a mean score of 151 with a standard deviation of 9 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 9 students at a time. A larger organization
> Chapter 2, Exercise 16 showed the histogram of the European shoe sizes from a sample of 269 college students. Looking at the men only, a 95% confidence interval for the mean shoe size shows: The student knows that European shoes are sized only in whole a
> Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What wrong with the others? 1. t-interval for μ:with 90.00% Confidence,43454
> Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a ma
> A survey finds that a 95% confidence interval for the mean salary of a police patrol officer in Fresno, California, in 2016 is $52,516 to $53,509. A student is surprised that so few police officers make more than $53,500. Explain what is wrong with the s
> For the confidence interval you found in Exercise 11 , interpret this interval and explain what 95% confidence means in this context.
> In the previous exercise, you found a 95% confidence interval to estimate the average loss in home value. 1. Suppose the standard deviation of the losses had been $3000 instead of $1500. What would the larger standard deviation do to the width of the con
> The housing market recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 36 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss from the peak i
> Describe how the critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases.
> A National Vital Statistics Report (www.cdc.gov/nchs/) provides information on deaths by age, sex, and race. Below are displays of the distributions of ages at death for White and Black males: 1. Describe the overall shapes of these distributions. 2. How
> A specialty food company sells whole King Salmon to various customers. The mean weight of these salmon is 35 pounds with a standard deviation of 2 pounds. The company ships them to restaurants in boxes of 4 salmon, to grocery stores in cartons of 16 salm
> The philanthropic organization in Exercise 3 expects about a 5% success rate when they send fundraising letters to the people on their mailing list. In Exercise 3, you looked at the histograms showing distributions of sample proportions from 1000 simulat
> For her final project, Stacy plans on surveying a random sample of 50 students on whether they plan to go to Florida for spring break. From past years, she guesses that about 10% of the class goes. Is it reasonable for her to use a Normal model for the s
> According to a Pew Research survey, 27% of American adults are pessimistic about the future of marriage and the family. That is based on a random sample of about 1500 people. Is it reasonable for Pew Research to use a Normal model for the sampling distri
> Gallup regularly conducts a poll using a Cantril scale, which asks respondents to imagine a ladder with 10 rungs. Rung 0 represents the worst possible life, and rung 10 represents the best possible life. Respondents are asked what rung they would say the
> Pew Research, in 2015, polled a random sample of 1060 U.S. teens (ages 13–17) about Internet use. 56% of those teens reported going online several times a day a fact of great interest to advertisers. 1. Explain the meaning of p^=0.56 in the context of
> An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the company did a simulation using samples of size 20, 50, 75
> When they send out their fundraising letters, a philanthropic organization typically gets a return from about 5% of the people on their mailing list. To see what the response rate might be for future appeals, they did a simulation using samples of size 2
> In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days. 1. How many randomly selected employers must we contact in order to create an estimate in which we are 98%
> The proportion of adult women in the United States is approximately 51%. A marketing survey telephones 400 people at random. 1. What proportion of the sample of 400 would you expect to be women? 2. What would the standard deviation of the sampling distri
> National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its findings in Vital and Health Statistics. Data from a sample of 39 male patients and 35 female patients on length of stay (in d
> It believed that as many as 25% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. 1. How many of this younger age group must we survey in order to estimate the proportion of no
> In Exercise 14, we saw that 53% of surveyed parents don’t spank their children. 1. Are the conditions for constructing a confidence interval met? 2. Would the margin of error be larger or smaller for 95% confidence? Explain.
> Consider the poll of Exercise 15. 1. Are the assumptions and conditions met? 2. Would the margin of error be larger or smaller for 95% confidence? Explain.
> The Gallup Poll described in Exercise 6 also asked about smoking. Only 18% of those polled reported that they smoked. 1. Calculate the margin of error for the proportion of all American adults who smoke with 99% confidence. 2. Explain in a simple sentenc
> An Ipsos/Reuters poll of 2214 U.S. adults voters in April and May 2017 asked a standard polling question of whether the United States was headed in the Right Direction or was on the Wrong Track. 54% said that things are on the wrong track vs. 33% who sai
> In a 2015 Pew Research study on trends in marriage and family (www.pewsocialtrends.org/2015/12/17/1-the-american-family-today/), 53% of randomly selected parents said that they never spank their children. The 95% confidence interval is from 50.6% to 55.4
> The 95% confidence interval for the number of teens in Exercise 5 who reported that they went online several times daily is from 53% to 59%. 1. Interpret the interval in this context. 2. Explain the meaning of 95% confident in this context.
> 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 distribution of scores on a statistics test for a particular class is skewed to the left. The professor wants to predict the maximum score and so wants to understand the distribution of the sample maximum. She simulates the distribution of the maximu
> The automatic character recognition device discussed in Exercise 4 successfully reads about 85% of handwritten credit card applications. In Exercise 4, you looked at the histograms showing distributions of sample proportions from 1000 simulated samples o
> Shown below are the histogram and summary statistics for the number of camp sites at public parks in Vermont: 1. Which statistics would you use to identify the center and spread of this distribution? Why? 2. How many parks would you classify as outliers?
> An investment company is planning to upgrade the mobile access to their website, but they’d like to know the proportion of their customers who access it from their smartphones. They draw a random sample of 200 from customers who recently logged in and ch
> A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digital TV service the company has provided. All numbers are in the 452 exchange, so there are 10,000 possible numbers from 452-0000
> A large hospital has an average of 7 fatalities in a week. Using the Poisson model, what is the probability that this week it has 10 fatalities?
> A car dealership sells an average of 5 cars in a day. Using the Poisson model, what is the probability that the dealer sells 3 cars tomorrow?
> If this team has 200 corner kicks over the season, what are the chances that they score more than 22 times?
> In a batch of 10,000 toasters, what are the chances that fewer than 450 need to be returned?
> A soccer team estimates that they will score on 8% of the corner kicks. In next week game, the team hopes to kick 15 corner kicks. What are the chances that they will score on 2 of those opportunities?
> A manufacturer ships toasters in cartons of 20. In each carton, they estimate a 5% chance that one of the toasters will need to be sent back for minor repairs. What is the probability that in a carton, there will be exactly 3 toasters that need repair?
> Do these situations involve Bernoulli trials? Explain. 1. You are rolling 5 dice and need to get at least two 6 to win the game. 2. We record the distribution of eye colors found in a group of 500 people. 3. A manufacturer recalls a doll because about 3%
> Suppose occurrences of sales on a small company website are well modeled by a Poisson model with λ=5/hour. 1. If a sale just occurred, what is the expected waiting time until the next sale? 2. What is the probability that the next sale will happen in th
> Below is a back-to-back stem-and-leaf display that shows two datasets at once one going to the left, one to the right. The display compares the percent change in population for two regions of the United States (based on census figures for 2000 and 2010).
> Lifetimes of electronic components can often be modeled by an Exponential model. Suppose quality control engineers want to model the lifetime of a hard drive to have a mean lifetime of 3 years. 1. What value of λ should they use? 2. With this model, wha
> Do these situations involve Bernoulli trials? Explain. 1. We roll 50 dice to find the distribution of the number of spots on the faces. 2. How likely is it that in a group of 120 the majority may have Type A blood, given that Type A is found in 43% of th
> 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 les
> 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?
> 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 deviatio
> 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 salarie
> What is the standard deviation for Exercise 2 ?
> What is the standard deviation for Exercise 1 ?
> A coffee shop tracks sales and has observed the distribution in the following table. What is the average daily sales that it can expect?
> People with spinal cord injuries may lose function in some, but not all, of their muscles. The ability to push oneself up is particularly important for shifting position when seated and for transferring into and out of wheelchairs. Surgeons compared two
> A citrus farmer has observed the following distribution for the number of oranges per tree. How many oranges does he expect on average?
> 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 tr
> 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.
> 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.
> 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?
> 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?
> From Exercise 3, if someone doesn’t like to watch basketball, what is the probability that she will be a football fan?
> What is the probability that a person likes to watch football, given that she also likes to watch basketball?
> Forty-five percent of Americans like to cook and 59% of Americans like to shop, while 23% enjoy both activities. What is the probability that a randomly selected American either enjoys cooking or shopping or both?
> Given the probabilities in Exercise 12, what is the probability that a person is younger than 50 given that she uses online banking? Has the probability that she is younger than 50 increased or decreased with the additional information?
> Sugar is a major ingredient in many breakfast cereals. The histogram displays the sugar content as a percentage of weight for 49 brands of cereal. The boxplots compare sugar content for adult and children cereals. 1. What is the range of the sugar conten
> Given the probabilities in Exercise 11, what is the probability that a person is from the United States given that he logs on to Facebook every day? Has the probability that he is from the United States increased or decreased with the additional informat
> Suppose that the information in Exercise 10 had been presented in the following way. A national survey of bank customers finds that 40% are younger than 50. Of those younger than 50, 5 of 8 conduct their banking online. Of those older than 50, only 1 of
> Suppose that the information in Exercise 9 had been presented in the following way. Facebook reports that 70% of its users are from outside the United States. Of the U.S. users, two-thirds log on every day. Of the non-U.S. users, three-sevenths log on ev
> A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are younger than 50, and that 25% are younger than 50 and conduct their banking online. Make a probability table. Why is a table better than a tree here?
> Suppose that 25% of people have a dog, 29% of people have a cat, and 12% of people own both. What is the probability that someone owns a dog or a cat?
> The survey by the National Center for Health Statistics further found that 49% of adults ages 25 29 had only a cell phone and no landline. We randomly select four 25 29-year-olds: 1. What is the probability that all of these adults have a only a cell pho
> A 2010 study conducted by the National Center for Health Statistics found that 25% of U.S. households had no landline service. This raises concerns about the accuracy of certain surveys, as they depend on random-digit dialing to households via landlines.
> Your list of favorite songs contains 10 rock songs, 7 rap songs, and 3 country songs. 1. What is the probability that a randomly played song is a rap song? 2. What is the probability that a randomly played song is not country?
> In your dresser are five blue shirts, three red shirts, and two black shirts. 1. What is the probability of randomly selecting a red shirt? 2. What is the probability that a randomly selected shirt is not black?
> After rolling doubles on a pair of dice three times in a row, your friend exclaims, I can’t get doubles four times in a row! Explain why this thinking is incorrect.
> The Men Giant Slalom skiing event consists of two runs whose times are added together for a final score. Two displays of the giant slalom times in the 2018 Winter Olympics at Pyeong Chang are shown below. 1. What features of the distribution can you see
> Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the li
> Your friend says: I flipped five heads in a row! The next one has to be tails! Explain why this thinking is incorrect.
> Rolling a fair six-sided die is supposed to randomly generate the numbers 1 through 6. Explain what random means in this context.
> Flipping a fair coin is said to randomly generate heads and tails with equal probability. Explain what random means in this context.
> Is the experiment of Exercise 3 blind? Can it be double-blind? Explain.
> For the experiment of Exercise 4, discuss variables that could be controlled or that could not be controlled. Is the experiment randomized and replicated?
> For the experiment of Exercise 3, name some variables the driver did or should have controlled. Was the experiment randomized and replicated?
> For the experiment described in Exercise 4, name the factor and its levels. How might the response be measured?
> For the experiment described in Exercise 3, list the factor, the levels, and the response variable.
> You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning the
> A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer ser
> Crowd Management Strategies (www.crowdsafe.com) monitors accidents at rock concerts. In their database, they list the names and other variables of victims whose deaths were attributed to crowd crush at rock concerts. Here are the histogram and boxplot of
> A business student conjectures that the Internet caused companies to become more profitable, since many transactions previously handled face-to-face could now be completed online. The student compares earnings from a sample of companies from the 1980s to
> What factors might confound the results of the experiment in Exercise 4?
> For the experiment of Exercise 3, name some confounding variables that might influence the experiment results.
> To obtain enough plants for the tomato experiment of Exercise 4, experimenters have to purchase plants from two different garden centers. They then randomly assign the plants from each garden center to all three fertilizer treatments. Is the experiment b
> The driver of Exercise 3 wants to know about tipping in general. So he recruits several other drivers to participate in the experiment. Each driver randomly decides whether to phone customers before delivery and records the tip percentage. Is this experi
> If the tomato taster doesn’t know how the tomatoes have been treated, is the experiment single- or double-blind? How might the blinding be improved further?
> The 1990s and early 2000s could be considered the steroids era in Major League Baseball, as many players have admitted to using the drug to increase performance on the field. If a sports writer wanted to compare home run totals from the steroids era to a
> What problems do you see with asking the following question of students? Are you the first member of your family to seek higher education?
