Question: The random variable in Exercise 7.30

> Currently Ebay lists over 550,000 U.S. collector coins for sale or auction. An avid collector tracked the number of days it took for 500 coins to be sent to his home. Create a histogram of these figures. What information can you draw from the shape of th

> A survey of golfers asked the following questions. Identify the type of data each question produces. a. How many rounds of golf do you play annually? b. Are you a member of a private club? c. What brand of clubs do you own?

> An Internet pharmacy advertises that it will deliver the over-the-counter products that customers purchase in 3–6 days. The manager of the company wanted to be more precise in its advertising. Accordingly, she recorded the number of day

> Baseball fans are regularly asked to offer their opinions about various aspects of the sport. A survey asked the following questions. Identify the type of data. a. How many games do you attend annually? b. How would you rate the quality of entertainment?

> Information about a magazine’s readers is of interest to both the publisher and the magazine’s advertisers. A survey of readers asked respondents to complete the following: a. Age b. Gender c. Marital status d. Number of magazine subscriptions e. Annual

> A survey of the business school graduates undertaken by a university placement office asked, among other questions, in which area each person was employed. The areas of employment are as follows: 1. Accounting 2. Finance 3. General management 4. Marketin

> The annual incomes for a sample of 200 first-year accountants were recorded. Draw a histogram and describe its shape.

> There are several ways to teach applied statistics. The most popular approaches are as follows: 1. Emphasize manual calculations. 2. Use a computer combined with manual calculations. 3. Use a computer exclusively with no manual calculations. A survey of

> The Wilfrid Laurier University bookstore conducts annual surveys of its customers. One question asks respondents to rate the prices of textbooks. The wording is, “The bookstore’s prices of textbooks are reasonable.” The responses are as follows: 1. Stro

> Refer to Exercise 2.59. The percentage of uninsured in 2013 and 2014 in each of the 50 states plus District of Columbia was recorded. Use a graphical technique to show the decrease in the uninsured rate. Data from Exercise 2.59: The primary objective of

> A sample of shoppers at a mall was asked the following questions. Identify the type of data each question would produce. a. What is your age? b. How much did you spend? c. What is your marital status? d. Rate the availability of parking: excellent, good,

> The primary objective of the Affordable Care Act was to decrease the number of nonelderly without any health insurance. It is estimated that there are still approximately 40 million Americans without health insurance. Researchers asked a sample of them w

> The Consumer Expenditure Survey measures how consumers allocate their spending. A recent survey asked respondents to specify the amount of their budget spent on food, housing, transportation, healthcare, and insurance and pensions. Also recorded were the

> The random variable X has the following probability distribution. Find the following probabilities. a. P(X > 0) b. P(X ≥ 1) c. P(X ≥ 2) d. P(2 ≤ X ≤ 5) -3 2 8 P(x) .2 3 .4

> It is recommended that women age 40 and older have a mammogram annually. A recent report indicated that if a woman has annual mammograms over a 10-year period, there is a 60% probability that there will be at least one false-positive result. (A false-pos

> According to a Gallup Poll conducted in 2015 only 1% of Russians approved of U.S. leadership. To evaluate whether this claim has any merit a statistician took a random sample of 100 Russians. Determine the probability of these events. a. No one approved

> When Earth traveled through the storm of meteorites trailing the comet Tempel-Tuttle on November 17, 1998, the storm was 1,000 times as intense as the average meteor storm. Before the comet arrived, telecommunication companies worried about the potential

> An investor hears a radio report that says in 60% of the stocks on the New York Stock Exchange increased in value. He realizes that he owns 20 stocks on the NYSE. Determine the probability of the following events. a. 15 or more stocks increased in value.

> In Basketball players are awarded free throw when they are fouled. Suppose that a player has a career percentage of making free throws 80% of the time. If the player is awarded 10 free throws determine the probability of the following events. a. He makes

> In 1941 Joe DiMaggio hit in 56 consecutive games, a record that is predicted to never be broken. To see how unlikely this streak was, assume that a player batting .350 gets to bat 5 times in a game (with no walks and hit by pitch). a. What is the probabi

> Advertising researchers have developed a theory that states that commercials that appear in violent television shows are less likely to be remembered and will thus be less effective. After examining samples of viewers who watch violent and nonviolent pro

> A pharmaceutical researcher working on a cure for baldness noticed that middle-aged men who are balding at the crown of their head have a 45% probability of suffering a heart attack over the next decade. In a sample of 100 middle-age balding men, what ar

> Researchers at the University of Pennsylvania School of Medicine theorized that children under 2 years old who sleep in rooms with the light on have a 40% probability of becoming myopic by age 16. Suppose that researchers found 25 children who slept with

> According to climatologists, the long-term average for Atlantic storms is 9.6 per season (June 1 to November 30), with 6 becoming hurricanes and 2.3 becoming intense hurricanes. Find the probability of the following events. a. Ten or more Atlantic storms

> Second-year business students at many universities are required to take 10 one-semester courses. The number of courses that result in a grade of A is a discrete random variable. Suppose that each value of this random variable has the same probability. De

> Most Miami Beach restaurants offer “early-bird” specials. These are lower-priced meals that are available only from 4 to 6 p.m. However, not all customers who arrive between 4 and 6 p.m. order the special. In fact, only 70% do. a. Find the probability th

> Shutouts in the National Hockey League occur randomly and independently at a rate of 1 every 20 games. Calculate the probability of the following events. a. 2 shutouts in the next 10 games b. 25 shutouts in 400 games c. A shutout in tonight’s game

> An auditor is preparing for a physical count of inventory as a means of verifying its value. Items counted are reconciled with a list prepared by the storeroom supervisor. In one particular firm, 20% of the items counted cannot be reconciled without revi

> Many cell phone service providers offer family plans wherein parents who subscribe can get discounts for other family members. Suppose that the number of cell phones per family is Poisson distributed with a mean of 1.5. If one family is randomly selected

> University and college students are relatively confident about finding a job after graduation. According to a Gallup survey 50% of students are say now is a good time to find a quality job. Suppose you randomly select 10 students and ask about their futu

> Ten percent of American adults devote so much time to playing video games either on a console, computer, or cell phone that they consider themselves to be “gamers” according to a Pew Research Center report. Suppose that a random sample of 25 American adu

> The Powerball lottery is one of the most popular lotteries in the United States. From time to time, the jackpot exceeds $100 million. As a result so many more people buy Powerball tickets that there are frequent lineups at convenience stores. A statistic

> Has the educational level of adults changed over the past 15 years? To help answer this question the Bureau of Labor Statistics compiled the following table, which lists the number (1,000) of adults 25 years of age and older who are employed. Use a graph

> Lotteries are an important income source for various governments around the world. However, the availability of lotteries and other forms of gambling have created a social problem: gambling addicts. A critic of government-controlled gambling contends tha

> Hikers and other outdoor enthusiasts have a new concern, the Zika virus. Physicians are recommending that people use a mosquito repellant while in areas where mosquitoes are present. A statistician estimated that 80% of hikers would be spraying themselve

> Using historical records, the personnel manager of a plant has determined the probability distribution of X, the number of employees absent per day. It is a. Find the following probabilities. P(2 ≤ X ≤ 5) P(X >

> The number of arrivals at a car wash is Poisson distributed with a mean of eight per hour. a. What is the probability that 10 cars will arrive in the next hour? b. What is the probability that more than 5 cars will arrive in the next hour? c. What is the

> Gallup Organization Date: May 2016 Population: American adults Question: “Please tell me whether you strongly favor or strongly oppose keeping the Affordable Care Act in place. Responses: 1. Favor 2. Oppose 3. No opinion Use a graphical technique to summ

> The final exam in a one-term statistics course is taken in the December exam period. Students who are sick or have other legitimate reasons for missing the exam are allowed to write a deferred exam scheduled for the first week in January. A statistics pr

> An airline boasts that 77.4% of its flights were on time. If we select five flights at random, what is the probability that all five are on time?

> A recent Pew Center Research survey revealed that 15% of American adults have used an online dating service. Suppose a statistician randomly selected 20 American adults. a. What is the probability that exactly 3 used an online dating service? b. What is

> In a Gallup poll 20% of adults said that they had a great deal or quite a lot of confidence in newspapers. If we take a random sample of 25 adults and ask each whether they had a great deal or quite a lot of confidence in newspapers determine probability

> The number of users of an automatic banking machine is Poisson distributed. The mean number of users per 5-minute interval is 1.5. Find the probability of the following events. a. No users in the next 5 minutes b. Five or fewer users in the next 15 minut

> Cars arriving for gasoline at a particular gas station follow a Poisson distribution with a mean of 5 per hour. a. Determine the probability that over the next hour only one car will arrive. b. Compute the probability that in the next 3 hours more than 2

> The number of trucks crossing at the Ambassador Bridge connecting Detroit, Michigan, and Windsor, Ontario, is Poisson distributed with a mean of 1.5 per minute. a. What is the probability that in any 1-minute time span two or more trucks will cross the b

> After conducting a survey of golfers a statistician concludes that the number of lost balls in a round is Poisson distributed with a mean of 2. Find the probability of the following events. a. A golfer loses no golf balls b. A golfer loses 4 or more no g

> In a recent census, the number of color televisions per household was recorded. a. Develop the probability distribution of X, the number of color televisions per household. b. Determine the following probabilities. P(X ≤ 2) P(X >

> The random variable in Exercise 7.44 was the number of holes in one by the members of a private golf course. In fact, the number of holes in one is Poisson distributed with a mean of 1. a. What proportion of members never have had a hole in one? b. What

> At a public library one of the librarians surveys individuals reading online newspapers. After analyzing the data she concludes that the number of newspapers read online is Poisson distributed with a mean of 5. a. What proportion of library patrons read

> At an auction of antique furniture a statistician kept track of the number of bids for each item. After an analysis of the figures she concludes that the number of bids is Poisson distributed with a mean of 2.5. a. Calculate the probability that on any i

> Flaws in a carpet tend to occur randomly and independently at a rate of one every 200 square feet. What is the probability that a carpet that is 8 feet by 10 feet contains no flaws?

> The number of bank robberies that occur in a large North American city is Poisson distributed with a mean of 1.8 per day. Find the probabilities of the following events. a. Three or more bank robberies in a day. b. Between 10 and 15 (inclusive) robberies

> In older cities across North America, infrastructure is deteriorating, including water lines that supply homes and businesses. A report to the Toronto city council stated that there are on average 30 water line breaks per 100 kilometers per year in the c

> Hits on a personal website occur quite infrequently. They occur randomly and independently with an average of five per week. a. Find the probability that the site gets 10 or more hits in a week. b. Determine the probability that the site gets 20 or more

> The number of students who seek assistance with their statistics assignments is Poisson distributed with a mean of two per day. a. What is the probability that no students seek assistance tomorrow? b. Find the probability that 10 students seek assistance

> Snowfalls occur randomly and independently over the course of winter in a Minnesota city. The average is one snowfall every 3 days. a. What is the probability of five snowfalls in 2 weeks? b. Find the probability of a snowfall today.

> Let X be the random variable designating the number of spots that turn up when a balanced die is rolled. What is the probability distribution of X?

> The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.5 per week. Find the probability of the following events. a. No accidents in one week b. Five or more accidents in one week c. One accident today

> Given that X is a Poisson random variable with = .5, use the formula to determine the following probabilities. a. P(X = 0) b. P(X = 1) c. P(X = 2)

> Given a Poisson random variable with  = 2, use the formula to find the following probabilities. a. P(X = 0) b. P(X = 3) c. P(X = 5)

> In a recent Gallup poll 53% of American adults believed that Congress is doing a poor or bad job. Suppose that you randomly choose 100 American adults and ask their opinion about Congress. a. Determine the probability that more than half say that Congres

> The statistics practitioner in Exercise 7.116 also determined that if a batter hits a line drive, the probability of an out is 23%. Determine the following probabilities. a. In a game with 10 line drives, at least 5 are outs. b. In a game with 25 line dr

> In a Bon Appetit poll, 38% of people said that chocolate was their favorite flavor of ice cream. A sample of 20 people was asked to name their favorite flavor of ice cream. What is the probability that half or more of them prefer chocolate?

> According to a Gallup Poll 52% of American adults think that protecting the environment should be given priority over developing U.S. energy supplies. Thirty-six percent think that developing energy supplies is more important, and 6% believe the two are

> In the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 25 times, find the probabilities of the following events. a. The ball falls into the green slots two or more times. b. T

> Researchers have developed statistical models based on financial ratios that predict whether a company will go bankrupt over the next 12 months. In a test of one such model, the model correctly predicted the bankruptcy of 85% of firms that did in fact fa

> The owner of an appliance store is interested in the relationship between the price at which an item is sold (regular or sale price) and the customer’s decision on whether to purchase an extended warranty. After analyzing her records, s

> Determine whether each of the following is a valid probability distribution. a. x 0 1 2 3 P(x) .1 .3 .4 .1 b. x 5 −6 10 0 P(x) .01 .01 .01 .97 c. x 14 12 −7 13 P(x) .25 .46 .04 .24

> In the game of blackjack as played in casinos in Las Vegas, Atlantic City, and Niagara Falls, as well as in many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a h

> The probability of winning a game of craps (a dicethrowing game played in casinos) is 244/495. a. What is the probability of winning 5 or more times in 10 games? b. What is the probability of winning in 50 or more times in 100 games?

> According to a recent Gallop poll only 29% of American adults said they were satisfied with the way things are going in the United States. Suppose you randomly select 10 American adults and ask each whether they are satisfied with the way things are goin

> In a recent survey the Pew Research Center asked graduates of private universities whether they were satisfied with their current job and 72% said they were. Suppose you take a sample of four private university graduates and ask each whether they are sat

> A statistics practitioner working for major league baseball determined the probability that the hitter will be out on ground balls is .75. In a game where there are 20 ground balls, find the probability that all of them were outs.

> Dermatologists strongly recommend that people who are exposed to sunlight should either be covered up or put on sunscreen. Suppose that at a Florida condominium pool only a quarter of residents sit around the pool in the sun with no sunscreen. a. What is

> According to a Pew Research Center survey 30% of graduates who had student loans are delinquent (90 or more days behind in their payments. Suppose that a survey of 10 such graduates is taken. a. What is the probability that 3 are delinquent? b. What is t

> According to a Gallup poll 27% of American adults have confidence in banks. Suppose that you interview 5 Americans adults at random. a. What is the probability that 2 or fewer have confidence in banks? b. What is the probability that no one had confidenc

> A student majoring in accounting is trying to decide on the number of firms to which he should apply. Given his work experience and grades, he can expect to receive a job offer from 70% of the firms to which he applies. The student decides to apply to on

> The effect of an antidepressant drug varies from person to person. Suppose that the drug is effective on 80% of women and 65% of men. It is known that 66% of the people who take the drug are women. What is the probability that the drug is effective?

> A certain type of tomato seed germinates 90% of the time. A backyard farmer planted 25 seeds. a. What is the probability that exactly 20 germinate? b. What is the probability that 20 or more germinate? c. What is the probability that 24 or fewer germinat

> A construction company has bid on two contracts. The probability of winning contract A is .3. If the company wins contract A, then the probability of winning contract B is .4. If the company loses contract A, then the probability of winning contract B de

> A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events? a. One out of the n

> Pew Research Center conducted a survey of countries around the world and asked respondents whether they were having a typical day, a good day, or a bad day. The results and the number of respondents in Europe, Asia, and the United States are listed next.

> Refer to Exercise 6.86. The professor meets a student who has just graduated in less than five year. Determine the probability that he graduated with B.B.A. degree. Data from Exercise 6.86: A statistics professor was in the process of comparing the pass

> Refer to Exercise 6.85. An American under 40 tells you that he has student debt. What is the probability that he is managerial or professional? Data from Exercise 6.85: How many Americans under the age of 40 have student debts? A Pew Research Center atte

> Refer to Exercise 6.84. A respondent who disapproved of the way the EU handled the refugee issue was selected. Calculate the probability that the respondent is from Greece. Data from Exercise 6.84: Respondents in Greece, Hungary, and Poland were asked wh

> Given a binomial random variable with n = 6 and p = .2, use the formula to find the following probabilities. a. P(X = 2) b. P(X = 3) c. P(X = 5)

> Refer to Exercise 6.76. The researchers examined a child under 16 and discovered that he is myopic. What is the probability that he slept with the lights when he was under 2? Data from Exercise 6.76: Researchers at the University of Pennsylvania School O

> The Pap smear is the standard test for cervical cancer. The false-positive rate is .636; the false-negative rate is .180. Family history and age are factors that must be considered when assigning a probability of cervical cancer. Suppose that, after obta

> Given a binomial random variable with n = 10 and p = .3, use the formula to find the following probabilities. a. P(X = 3) b. P(X = 5) c. P(X = 8)

> The Rapid Test is used to determine whether someone has HIV (the virus that causes AIDS). The false-positive and false-negative rates are .027 and .080, respectively. A physician has just received the Rapid Test report that his patient tested positive. B

> Transplant operations have become routine. One common transplant operation is for kidneys. The most dangerous aspect of the procedure is the possibility that the body may reject the new organ. Several new drugs are available for such circumstances, and t

> Calculate the mean and standard deviation of the portfolio. The proportions invested in each stock are shown in parentheses. a. Intel (INTC): 25%, Oracle (ORCL): 25%, Sirius (SIRI): 25%, Starbucks (SBUX): 25% b. INTC: 10%, ORCL: 10%, SIRI: 10%, SBUX: 70%

> Calculate the mean and standard deviation of the portfolio. The proportions invested in each stock are shown in parentheses. a. Costco (COST): 25%, Dollar Tree (DLTR): 25%, Expedia (EXPE): 25%, ScanDisk (SNDK): 25% b. COST: 10%, DLTR: 20%, EXPE: 30%, SND

> Calculate the mean and standard deviation of the portfolio. The proportions invested in each stock are shown in parentheses. a. Amazon (AMZN): 25%, Apple (AAPL): 25%, Bed Bath and Beyond (BBBY): 25%, Dollar Tree (DLTR): 25% b. AMZN: 10%, AAPL: 40%, BBBY:

> Calculate the mean and standard deviation of the portfolio. The proportions invested in each stock are shown in parentheses. a. Adobe (ADBE): 25%, Cisco Systems (CSCO): 25%, Comcast (CMCSA): 25%, Garmin (GRMN): 25% b. ADBE: 40%, CSCO: 10%, CMCSA: 40%, GR

> Bad gums may mean a bad heart. Researchers discovered that 85% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums. Only 29% of healthy people have this disease. Suppose that in a certain community heart attack

> Refer to Exercise 6.74. A randomly selected candidate who took a CFA exam tells you that he has passed the exam. What is the probability that he took the CFA I exam? Data from Exercise 6.74: The chartered financial analyst (CFA) is a designation earned a

> Calculate the mean and standard deviation of the portfolio. The proportions invested in each stock are shown in parentheses. a. Agnico Eagle (AEM): 25%, Canadian Imperial Bank of Commerce (CM): 25%, Canadian Tire (CTC.A): 25%, Royal Bank (RY): 25% b. AEM

> In Case 6.2, we presented the probabilities of scoring at least one run and asked you to determine whether the manager should signal for the batter to sacrifice bunt. The decision was made on the basis of comparing the probability of scoring at least one

> If an intercompany profit is recorded on the sale of an asset to an affiliate within the consolidated entity in Period 1, when should this profit be considered realized? Explain.