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mathematics
statistics

Questions and Answers of Statistics

A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 20% of potential customers will choose the Day Plan, which does not include
Given independent random variables, X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the variables in parts a to d.a) 3Xb) Y + 6c) X+ Yd) X-Y
Suppose occurrences of sales on a small company’s website are well modeled by a Poisson model with A — 5/hour. a) If a sale just occurred, what it the expected waiting time until the next
In the first quarter of 2013, a group of domestic equity mutual funds had a mean return of 6.2% with a standard deviation of 1.8%. If a Normal model can be used to model them, what percent of the
Although controversial and the subject of some recent law suits (e.g., Satchell et al. vs. FedEx Express), some human resource departments administer standard IQ tests to all employees. The
From the mutual funds in Exercise 23 with quarterly returns that are well modeled by a Normal model with a mean of 6.2% and a standard deviation of 1.8%, find the cutoff return value(s) that would
For the IQ test administered by human resources and discussed in Exercise 24, what cutoff value would separate the a) Lowest 0.15% of all applicants? b) Lowest 16%? c) Middle 95%? d) Highest 2.5%?
The daily exchange rates for the five-year period 2008 to 2013 between the euro (EUR) and the British pound (GBP) can be modeled by a Normal distribution with mean 1.19 euros (to pounds) and standard
For the 300 trading days from January 11, 2012 to March 22, 2013, the daily closing price of IBM stock (in $) is well modeled by a Normal model with mean $197.92 and standard deviation $7.16.
For the model of the EUR/GBP exchange rate discussed in Exercise 27, what would the cutoff rates be that would separate the a) Highest 16% of EUR/GBP rates? b) Lowest 50%? c) Middle 95%? d) Lowest
According to the model in Exercise 28, what cutoff value of price would separate the a) Lowest 16% of the days? b) Highest 0.15%? c) Middle 68%? d) Highest 50%?
According to the Normal model N(0.062, 0.018) describing mutual fund returns in the 1st quarter of 2013 in Exercise 23, what percent of this group of funds would you expect to have return a) Over
Based on the Normal model N (100, 16) describing IQ scores from Exercise 24, what percent of applicants would you expect to have scores? a) Over 80? b) Under 90? c) Between 112 and 132? d) Over 125?
Based on the model Af(0.062, 0.018) for quarterly returns from Exercise 23, what are the cut-off values for the a) Highest 10% of these funds? b) Lowest 20%? c) Middle 40%? d) Highest 80%?
In the Normal model N(100, 16) for IQ scores from Exercise 24, what cutoff value bounds the a) Highest 5% of all IQs? b) Lowest 30% of the IQs? c) Middle 80% of the IQs? d) Lowest 90% of all IQs?
Consider the Normal model N(0.062, 0.018) for returns of mutual funds in Exercise 23 one last time. a) What value represents the 40th percentile of these returns? b) What value represents the 99th
Consider the IQ model N(100, 16) one last time. a) What IQ represents the 15th percentile? b) What IQ represents the 98th percentile? c) What’s the IQR of the IQs?
Every Normal model is defined by its parameters, the mean and the standard deviation. For each model described here, find the missing parameter. As always, start by drawing a picture. a) μ = 20, 45%
Every Normal model is defined by its parameters, the mean and the standard deviation. For each model described here, find the missing parameter. Don’t forget to draw a picture. a) μ = 1250, 35%
SAT or ACT? Each year thousands of high school students take either the SAT or ACT, standardized tests used in the college admissions process. Combined SAT scores can go as high as 1600, while the
Anna, a business major, took final exams in both Microeconomics and Macroeconomics and scored 83 on both. Her roommate Megan, also taking both courses, scored 77 on the Micro exam and 95 on the Macro
Suppose that job satisfaction scores can be modeled with N(100, 12). Human resource departments of corporations are generally concerned if the job satisfaction drops below a certain score. What score
Exercise 23 proposes modeling quarterly returns of a group of mutual funds with N(0.062, 0.018). The manager of this group of funds would like to flag any fund whose return is unusually low for a
A survey of 200 middle managers showed a distribution of the number of hours of exercise they participated in per week with a mean of 3.66 hours and a standard deviation of 4.93 hours. a) According
A large philanthropic organization keeps records on the people who have contributed to their cause. In addition to keeping records of past giving, the organization buys demographic data on
Manufacturing and selling drugs that claim to reduce an individual’s cholesterol level is big business. A company would like to market their drug to women if their cholesterol is in the top 15%.
A tire manufacturer believes that the tread life of its snow tires can be described by a Normal model with a mean of 32,000 miles and a standard deviation of 2500 miles. a) If you buy a set of these
Two companies make batteries for cell phone manufacturers. One company claims a mean life span of 2 years, while the other company claims a mean life span of 2.5 years (assuming average use of
The police department of a major city needs to update its budget. For this purpose, they need to under-stand the variation in their fines collected from motorists for speeding. As a sample, they
A business publication recently released a study on the total number of years of experience in industry among CEOs. The mean is provided in the article, but not the standard deviation. Is the
Your company will admit to the executive training program only people who score in the top 3 % on the executive aptitude test discussed in Exercise 3. a) With your 2-score of 2.20, did you make the
A newsletter for investors recently reported that the average stock price for a blue chip stock over the past 12 months was $72. No standard deviation was given. Is the standard deviation more likely
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
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
In Exercise 51 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
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 52. a)
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
The bicycle shop in Exercise 55 estimates using current labor costs that unpacking a bike costs $0.82 on average with a standard deviation of $0.16. Assembly costs $8.00 on average with a standard
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
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
A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The typical size of classes that meet there is 188, and we can assume that about 13% of students are
The pediatrician in Exercise 4 explains to the parents that the most extreme 5% of cases often require special treatment or attention. a) Does this child fall into that group? b) What do you need to
Police estimate that 80% of drivers wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. If they stop 120 cars, what’s the probability they find at least
Vitamin D is essential for strong, healthy bones. Although the bone disease rickets was largely eliminated in England during the 1950s, some people there are concerned that this generation of
A tennis player has taken a special course to improve her serving. She thinks that individual serves are independent of each other. She has been able to make a successful first serve 70% of the time.
Defects can occur anywhere on the wheel of a car during the manufacturing process. If X is the angle where the defect occurs, measured from a reference line, then X can be modeled as a uniform random
My employee seems to leave work anytime between 5PM and 6PM, uniformly. a) What is the probability he will still be at work at 5:45 PM? b) What is the probability he will still be at work at 5:45 PM
A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent
A cell phone manufacturer samples cell phones from the assembly to test. She noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of
The Environmental Protection Agency (EPA) fuel economy estimates for automobiles suggest a mean of 24.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume that a Normal model can be
Some IQ tests are standardized to a Normal model with a mean of 100 and a standard deviation of 16. a) Draw the model for these IQ scores. Clearly label it, showing what the 68-95-99.7 Rule predicts
What percent of a standard Normal model is found in each region? Be sure to draw a picture first. a) 2 > 1.5 b) 2 < 2.25 c) -1 < 2 < 1.15 d) 121 > 0.5
An incoming MBA student took placement exams in economics and mathematics. In economics, she scored 82 and in math 86. The overall results on the economics exam had a mean of 72 and a standard
What percent of a standard Normal model is found in each region? Draw a picture first. a) 2 > —2.05 b) 2 < -0.33 c) 1.2 < 2 < 1.8 d) |z| < 1.28
In a standard Normal model, what value(s) of 2 cut(s) off the region described? Don’t forget to draw a picture. a) The highest 20% b) The highest 75% c) The lowest 3 % d) The middle 90%
In a standard Normal model, what value(s) of 2 cut(s) off the region described? Remember to draw a picture first. a) The lowest 12 % b) The highest 30% c) The highest 7% d) The middle 50%
Has the Consumer Price Index (CPI) fluctuated around its mean according to a Normal model? Here are some displays. Is a Normal model appropriate for these data? Explain.
For a new type of tire, a NASCAR team found the average distance a set of tires would run during a race is 168 miles, with a standard deviation of 14 miles. Assume that tire mileage is independent
In the 4 X 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
Because many passengers who make reservations do not show up, airlines often overbook flights (sell more tickets than there are seats). A Boeing 767-400ER holds 245 passengers. If the airline
Shortly after the introduction of the Belgian euro coin, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin
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
The first Statistics exam had a mean of 65 and a stan¬dard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Julie scored
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’s production run, which produced cell phones with
Indicate whether each statement below is true or false. If false, explain why. a) We can eliminate sampling error by selecting an unbiased sample. b) Randomization helps to ensure that our sample is
A question posted on the Lycos website asked visitors to the site to say whether they thought that businesses should be required to pay for their employees’ health insurance. a) The population b)
An intern for the environmental group in Exercise 3 has decided to make the survey process simpler by calling 150 of the members who attended the recent symposium on coping with climate change that
The airline company in Exercise 4 has realized that some of its customers don’t have e-mail or don’t read it regularly. They decide to restrict the mailing only to customers who have recently
An intern is working for Pacific TV (PTV), a small cable and Internet provider, and has proposed some questions that might be used in the survey to assess whether customers are willing to pay $50 for
Indicate whether each statement below is true or false. If false, explain why. a) A local television news program that asks viewers to call in and give their opinion on an issue typically results in
Indicate whether each statement below is true or false. If false, explain why. a) Asking viewers to call into an 800 number is a good way to produce a representative sample. b) When writing a survey,
For your marketing class, you’d like to take a survey from a sample of all the Catholic Church members in your city to assess the market for a DVD about Pope Francis’s first year as pope. A list
The U.S. Fish and Wildlife Service plans to study the fishing industry around Saginaw Bay. To do that, they decide to randomly select five fishing boats at the end of a randomly chosen fishing day
The website www.gamefaqs.com asked, as their question of the day to which visitors to the site were invited to respond, “Do you ever read the end-user license agreements when installing software or
Indicate whether each statement below is true or false. If false, explain why. a) To get a representative sample, you must sample a large fraction of the population. b) Using modern methods, it is
Major League Baseball responding to concerns about their “brand” tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug-testing
Pew Research Center publishes polls on issues important in the news and about American life at its website, www.pewinternet.org. At the end of a report about a survey you can find a paragraph such as
At its website (www.gallup.com) the Gallup World Poll reports results of surveys conducted in various places around the world. At the end of one of these reports about the reliability of electric
Pew Internet & American Life Project surveyed 802 pairs of parents and teens (aged 12-17). They report that 93% of teens have access to a computer. 25% of teens access the Internet primarily on their
The Gallup Poll interviewed 1022 randomly selected U.S. adults aged 18 and older, March 7-10, 2013. Gallup reports that when asked whether respondents thought that global warming was due primarily
Researchers waited outside a bar they had randomly selected from a list of such establishments. They stopped every tenth person who came out of the bar and asked whether he or she thought drinking
Hoping to learn what issues may resonate with voters in the coming election the campaign director for a mayoral candidate selects one block at random from each of the city’s election districts.
The Environmental Protection Agency took soil samples at 16 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any
Inspectors send trained “renters” of various races and ethnic backgrounds and of both sexes to inquire about renting randomly assigned advertised apartments. They look for evidence that landlords
A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day’s production and weighing the bags. Then they open one bag from each case and inspect the
An environmental advocacy group is interested in the perceptions of farmers about global climate change. Specifically, they wish to determine the percentage of organic farmers who are concerned that
Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed
A local TV station conducted an “Instant Poll” to predict the winner in the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced
Prior to the mayoral election discussed in Exercise 31, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area
A local cable TV com-pany, Pacific TV (PTV), with customers in 15 towns is considering offering high-speed Internet service on its cable lines. Before launching the new service they want to find out
Four new sampling strategies have been proposed to help PTV determine whether enough cable subscribers are likely to purchase high-speed Internet service. For each, indicate what kind of sampling
An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to three hours for a two-minute ride. Concerned about how patrons (who paid a large amount to enter
The survey of patrons waiting in line for the roller coaster in Exercise 35 asks whether they think it is worthwhile to wait a long time for the ride and whether they’d like the amusement park to
The survey described in Exercise 36 asked, Many people believe this playground is too small and in need of repair. Do you think the playground should be repaired and expanded even if that means
Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. a) Should companies that pollute the environment be
An airline company is interested in the opinions of their frequent flyer customers about their proposed new routes. Specifically they want to know what proportion of them plan to use one of their new
Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question. a) Do you think that price or quality is more important in
Anytime we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 p.m., and interview whoever
What about drawing a random sample only from cell phone exchanges? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from
How much change do you have on you right now? Go ahead, count it. a) Suppose you check on your change every day for a week as you head for lunch and average the results. What parameter would this

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