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Essentials Of Business Statistics Communicating With Numbers 1st Edition Sanjiv Jaggia, Alison Kelly - Solutions
The revised guidelines from the National High Blood Pressure Education Program define normal blood pressure as readings below 120/80 millimeters of mercury (The New York Times, May 14, 2003). Prehypertension is suspected when the top number (systolic) is between 120 and 139 or when the bottom
U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,790 (Kiplinger's , August 2007). Assume that the average amount spent on a debit card is normally distributed with a standard deviation of
On St. Patrick's Day, men spend an average of $43.87 while women spend an average of $29.54 (USA TODAY, March 17, 2009). Assume the standard deviations of spending for men and women are $3 and $11, respectively, and that both distributions are normally distributed. a. What is the probability that
Lisa Mendes and Brad Lee work in the sales department of an AT&T Wireless Store. Lisa has been signing in an average of 48 new cell phone customers every month with a standard deviation of 22, while Brad signs in an average of 56 new customers with a standard deviation of 17. The store manager
The length of components produced by a company is normally distributed with a mean of 6 cm and a standard deviation of 0.02 cm. Calculate the 1st, 2nd, and 3rd quartiles of the component length.
A new water filtration system is sold with a 10-year warranty that includes all parts and repairs. Suppose the life of this water filtration system is normally distributed with mean and standard deviation of 16 and 5 years, respectively.a. What is the probability that the water iltration system
Suppose that the average IQ score is normally distributed with a mean of 100 and a standard deviation of 16. In addition to providing the answer, state the relevant Excel commands.a. What is the probability a randomly selected person will have an IQ score of less than 80?b. What is the probability
Suppose that the annual household income in a small mid western community is normally distributed with a mean of $55,000 and a standard deviation of $4,500. In addition to providing the answer, state the relevant Excel commands.a. What is the probability that a randomly selected household will have
On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeders.Assume the time that elapses between successive speeders is exponentially distributed with a mean of 15 minutes.a. Calculate the rate parameter f.b. What is the probability of a
According to the Federal Bureau of Investigation, there is a violent crime in the United States every 22 seconds (ABC News, September 25, 2007). Assume that the time between successive violent crimes is exponentially distributed. a. What is the probability that there is a violent crime in the
In a local law office, jobs to a printer are sent at a rate of 8 jobs per hour. Suppose that the number of jobs sent to a printer follows the Poisson distribution.a. What is the expected time between successive jobs?b. What is the probability that the next job will be sent within five minutes?
Disturbing news regarding Scottish police concerns the number of crashes involving vehicles on operational duties (BBC News, March 10, 2008). Statistics showed that Scottish forces'vehicles had been involved in traffic accidents at the rate of 1,000 per year. Suppose the number of crashes involving
A large technology firm receives an average of 12 new job applications every 10 days for positions that are not even advertised. Suppose the number of job applications received follows a Poisson distribution.a. What is the average number of days between successive job applications?b. What is the
The mileage (in 1,000s of miles) that car owners get with a certain kind of radial tire is a random variable having an exponential distribution with a mean of 50. In addition to providing the answer, state the relevant Excel commands.a. What is the probability that a tire will last at most 40,000
On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. In addition to providing the answer, state the relevant Excel commands.a. What is the probability that the appliance will work no more than
The Netherlands is one of the world leaders in the production and sale of tulips. Suppose the heights of the tulips in the greenhouse of Rotterdam’s Fantastic Flora follow a continuous uniform distribution with a lower bound of 7 inches and an upper bound of 16 inches. You have come to the
A random variable X is exponentially distributed with a probability density function of f (x) = 5e-5x. Calculate the mean and the standard deviation of X.
A tollbooth operator has observed that cars arrive randomly at an average rate of 360 cars per hour.a. What is the mean time between car arrivals at this tollbooth?b. What is the probability that the next car will arrive within ten seconds?
The car speeds on a certain stretch of the interstate highway I-95 are known to be normally distributed with a mean of 72 and a standard deviation of 15. You have just heard a policeman comment that about 3% of the drivers drive at extremely dangerous speeds. What range of speeds is he referring to?
The average household income in a community is known to be $80,000. Also, 20% of the households have an income below $60,000 and anoher 20% have income above $90,000. Is it reasonable to use the normal distribution to model the household income in this community?
Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 420 and a standard deviation of 80. Parul Monga is trying
Body mass index (BMI) is a reliable indicator of body fat for most children and teens. BMI is calculated from a child’s weight and height and is used as an easy-to-perform method of screening for weight categories that may lead to health problems. For children and teens, BMI is age- and
In the introductory case of Chapter 3 we discussed Vanguard’s Precious Metals and Mining fund (Metals) and Fidelity’s Strategic Income fund (Income), which were two top-performing mutual funds for the years 2000 through 2009. An analysis of annual return data for these two funds provided
A variety of packaging solutions exist for products that must be kept within a specific temperature range. A cold chain distribution is a temperature-controlled supply chain. An unbroken cold chain is an uninterrupted series of storage and distribution activities that maintain a given temperature
In 2010, Apple introduced the iPad, a tablet-style computer that its former CEO Steve Jobs called a" a truly magical and revolutionary product" (CNN, January 28, 2010). Suppose you are put in charge of determining the age profile of people who purchased the iPad in the United States. Explain in
A marketing firm opens a small booth at a local mall over the weekend, where shoppers are asked how much money they spent at the food court. The objective is to determine the average monthly expenditure of shoppers at the food court. Has the marketing firm committed any sampling bias? Discuss.
Natalie Min is a business student in the Haas School of Business at Berkeley. She wishes to pursue an MBA from Berkeley and wants to know the profile of other students who are likely to apply to the Berkeley MBA program. In particular, she wants to know the GPA of students with whom she might be
Vons, a large supermarket in Grover Beach, California, is considering extending its store hours from 7:00 am to midnight, seven days a week, to 6:00 am to midnight. Discuss the sampling bias in the following sampling strategies: a. Mail a prepaid envelope to randomly selected residents in the
In the previous question regarding Vons's store hours, explain how you can obtain a representative sample based on the following sampling strategies: a. Simple random sampling. b. Stratified random sampling. c. Cluster sampling. σ = .
A random sample is drawn from a normally distributed population with mean µ =12 and standard deviation σ =1.5.a. Comment on the sampling distribution of the sample mean with n=20 and n=40.b. Can you use the standard normal distribution to calculate the probability that the sample mean is less
A random sample is drawn from a population with meanµ =66 and standard deviation σ =5.5.a. Comment on the sampling distribution of the sample mean with n=16 and n=36.b. Can you use the standard normal distribution to calculate the probability that the sample mean falls between 66 and 68 for both
A random sample of size n=100 is taken from a population with mean µ =80 and standard deviation σ =14. a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. b. What is the probability that the sample mean falls between 77 and 85? c. What is the
A random sample of size n = 50 is taken from a population with mean µ = - 9.5 and standard deviation σ =2. a. Calculate the expected value and the standard error for the sampling distribution of the sample mean. b. What is the probability that the sample mean is less than 210? c. What is the
According to a recent survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume the population standard deviation is 20 text messages. Suppose a random sample of 50 high school girls is taken. a. What is the probability that the sample mean is more than
Beer bottles are filled so that they contain an average of 330 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 4 ml.a. What is the probability that a randomly selected bottle will have less than 325 ml of beer?b. What is
Despite its nutritional value, seafood is only a tiny part of the American diet, with the average American eating just 16 pounds of seafood per year. Janice and Nina both work in the seafood industry and they decide to create their own random samples and document the average seafood diet in their
The weight of people in a small town in Missouri is known to be normally distributed with a mean of 180 pounds and a standard deviation of 28 pounds. On a raft that takes people across the river, a sign states, "Maximum capacity 3,200 pounds or 16 persons."What is the probability that a random
The weight of turkeys is known to be normally distributed with a mean of 22 pounds and a standard deviation of=pounds.a. Discuss the sampling distribution of the sample mean based on a random draw of 16 turkeys.b. find the probability that the mean weight of 16 randomly selected turkeys is more
A small hair salon in Denver, Colorado, averages about 30 customers on weekdays with a standard deviation of 6. It is safe to assume that the underlying distribution is normal. In an attempt to increase the number of weekday customers, the manager offers a $2 discount on=consecutive weekdays. She
Last year, the typical college student graduated with $27,200 in debt (The Boston Globe, May 27, 2012). Let debt among recent college graduates be normally distributed with a standard deviation of $7,000.a. What is the probability that the average debt of four recent college graduates is more than
A doctor is getting sued for malpractice by four of her former patients. It is believed that the amount that each patient will sue her for is normally distributed with a mean of $800,000 and a standard deviation of $250,000.a. What is the probability that a given patient sues the doctor for more
Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with a mean and a standard deviation of 33.8 and 3.5 mpg, respectively.a. What is the probability that a randomly selected passenger car gets more than 35 mpg?b. What is the probability that
Suppose that IQ scores are normally distributed with a mean of 100 and a standard deviation of 16.a. What is the probability that a randomly selected person will have an IQ score of less than 90?b. What is the probability that the average IQ score of four randomly selected people is less than 90?c.
Consider a population proportion p=0.68. a. Calculate the expected value and the standard error of P with n=20. Is it appropriate to use the normal distribution approximation for P? Explain. b. Calculate the expected value and the standard error of P with n=50. Is it appropriate to use the normal
Consider a population proportion p=0.12.a. Discuss the sampling distribution of the sample proportion with n=20 and n=50.b. Can you use the normal approximation to calculate the probability that the sample proportion is between 0.10 and 0.12 for both sample sizes?c. Report the probabilities if you
A random sample of size n=200 is taken from a population with population proportion p=0.75. a. Calculate the expected value and the standard error for the sampling distribution of the sample proportion. b. What is the probability that the sample proportion is between 0.70 and 0.80? c. What is the
A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5, 2010). Suppose a random sample of 100 teen drivers is taken.a. Discuss the sampling distribution of the sample proportion.b. What is the probability that the
According to a recent FCC survey, one in six cell phone users has experienced "bill shock" from unexpectedly high cell phone bills (Tech Daily Dose, May 26, 2010).a. Discuss the sampling distribution of the sample proportion based on a sample of 200 cell phone users. Is it appropriate to use the
A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 40 customers. The dealer will be fined if the number of customers who report favorably is between 22 and 26. The dealership will be
Europeans are increasingly upset at their leaders for making deep budget cuts to many social programs that are becoming too expensive to sustain. For instance, the popularity of then President Nicolas Sarkozy of France plummeted in 2010, giving him an approval rating of just 26% (The Wall Street
At a new exhibit in the Museum of Science, people are asked to choose between 50 or 100 random draws from a machine. The machine is known to have 60 green balls and 40 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than
After years of rapid growth, illegal immigration into the United States has declined, perhaps owing to the recession and increased border enforcement by the United States (Los Angeles Times, September 1, 2010). While its share has declined, California still accounts for 23% of the nation's
A and b. σ 30. A random sample of size n=100 is taken from a population of size N=2,500 with mean µ = 245 and variance σ- =81. a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of the sample mean. b. What is the
A random sample of size n=70 is taken from a finite population of size N=500 with mean µ = - 20 and variance σ2=324.a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of the sample mean.b. What is the probability that
A random sample of size n=100 is taken from a population of size N=3,000 with a population proportion of p=0.34.a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of the sample proportion.b. What is the probability that
A random sample of size n=80 is taken from a population of size N=600 with a population proportion p=0.46.a. Is it necessary to apply the finite population correction factor? Explain. Calculate the expected value and the standard error of the sample proportion.b. What is the probability that the
The issues surrounding the levels and structure of executive compensation have gained added prominence in the wake of the financial crisis that erupted in the fall of 2008.Based on the 2006 compensation data obtained from the Securities and Exchange Commission (SEC) website, it was determined that
Suppose in the previous question that the analyst had randomly chosen 12 CEO compensations for 2006.a. Is it necessary to apply the finite population correction factor? Explain.b. Is the sampling distribution of the sample mean approximately normally distributed? Explain.c. Calculate the expected
Given the recent economic downturn, only 60% in a graduating class of 250 will find employment in the first round of a job search. You have 20 friends who have recently graduated.a. Discuss the sampling distribution of the sample proportion of your friends who will find employment in the first
A recent study finds that companies are setting aside a large chunk of their IT spending for green technology projects (BusinessWeek, March 5, 2009). Two out of three of the large companies surveyed by Deloitte said they have at least 5% of their IT budget earmarked for green IT projects. Suppose
Consider a normally distributed population with mean µ =80 and standard deviation σ =14.a. Construct the centerline and the upper and lower control limits for the x chart if samples of size=are used.b. Repeat the analysis with samples of size 10.c. Discuss the effect of the sample size on the
Random samples of size n=25 are taken from a normally distributed population with mean µ =20 and standard deviation σ =10.a. Construct the centerline and the upper and lower control limits for the x chart.b. Suppose six samples of size 25 produced the following sample means: 18, 16, 19, 24, 28,
Random samples of size n=36 are taken from a population with mean µ =150 and standard deviation σ = 42.a. Construct the centerline and the upper and lower control limits for the x chart.b. Suppose five samples of size 36 produced the following sample means: 133, 142, 150, 165, and 169. Plot these
Random samples of size n=250 are taken from a population with p=0.04.a. Construct the centerline and the upper and lower control limits for the p chart.b. Repeat the analysis with n=150.c. Discuss the effect of the sample size on the control limits.
Random samples of size n=400 are taken from a population with p= 0.10.a. Construct the centerline and the upper and lower control limits for the p chart.b. Suppose six samples of size 400 produced the following sample proportions: 0.06, 0.11, 0.09, 0.08, 0.14, and 0.16.Plot these values on the p
Random samples of size n=500 are taken from a population with p=0.34.a. Construct the centerline and the upper and lower control limits for the p chart.b. Suppose six samples of size 500 produced the following sample proportions: 0.28, 0.30, 0.33, 0.34, 0.37, and 0.39.Plot these values on the p
A production process is designed to ill boxes with an average of 14 ounces of cereal. The population of filling weights is normally distributed with a standard deviation of 2 ounces. Inspectors take periodic samples of 10 boxes. The following sample means are obtained.a. Construct an x chart. Plot
Major League Baseball Rule 1.09 states that "the baseball shall weigh not less than=or more than=1⁄4 ounces" (www.mlb.com). Use these values as the lower and the upper control limits, respectively. Assume the centerline equals 5.125 ounces. Periodic samples of 50 baseballs produce the following
Fast bowling, also known as pace bowling, is an important component of the bowling attack in the sport of cricket. The objective is to bowl at a high speed and make the ball turn in the air and of the ground so that it becomes difficult for the batsman to hit it cleanly. Kalwant Singh is a budding
A firm produces computer chips for personal computers.From past experience, the firm knows that 4% of the chips are defective. The firm collects a sample of the first 500 chips manufactured at 1:00 pm for the past two weeks. The following sample proportions are obtained:a. Construct a p chart. Plot
A manufacturing process produces steel rods in batches of 1,000. The firm believes that the percent of defective items generated by this process is 5%.a. Construct the centerline and the upper and lower control limits for the p chart.b. An engineer inspects the next batch of 1,000 steel rods and
The college admissions office at a local university usually admits 750 students and knows from previous experience that 25% of these students choose not to enroll at the university.a. Construct the centerline and the upper and lower control limits for the p chart.b. Assume that this year the
Following customer complaints about the quality of service, Dell stopped routing corporate customers to a technical support call center in Bangalore, India (USA Today, November 24, 2003). Suppose Dell's decision to direct customers to call centers outside of India was based on consumer complaints
A seminal study conducted by scientists at the University of Illinois found evidence of improved memory and reasoning for those who took three vigorous 40-minute walks a week over six months (Newsweek, June 28-July 5, 2010). As an assistant manager working for a public health institute based in
In the previous question regarding walking regimens of the residents of Miami, explain how you can obtain a representative sample based on the following sampling strategies: a. Simple random sampling. b. Stratified random sampling. c. Cluster sampling.
According to the Bureau of Labor Statistics it takes an average of 22 weeks for someone over 55 to find a new job, compared with 16 weeks for younger workers (The Wall Street Journal, September 2, 2008). Assume that the probability distributions are normal and that the standard deviation is 2 weeks
While starting salaries have fallen for college graduates in many of the top hiring fields, there is some good news for business undergraduates with concentrations in accounting and finance (Bloomberg Business week, July 1, 2010). According to the National Association of Colleges and Employers'
An automatic machine in a manufacturing process is operating properly if the length of an important subcomponent is normally distributed with a mean µ =80 cm and a standard deviation σ =2 cm. a. find the probability that the length of one randomly selected unit is less than 79 cm. b. find the
Trader Joe's is a privately held chain of specialty grocery stores in the United States. Starting out as a small chain of convenience stores, it has expanded to over 340 stores as of June 2010 (Traderjoe.com). It has developed a reputation as a unique grocery store selling products such as gourmet
Georgia residents spent an average of $470.73 on the lottery in 2010, or 1% of their personal income (www.msn.com, May 23, 2012). Suppose the amount spent on the lottery follows a normal distribution with a standard deviation of $50.a. What is the probability that a randomly selected Georgian spent
Data from the Bureau of Labor Statistics' Consumer Expenditure Survey (CE) show that annual expenditures for cellular phone services per consumer unit increased from $210 in 2001 to $608 in 2007. Let the standard deviation of annual cellular expenditure be $48 in 2001 and $132 in 2007. a. What is
According to a recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy (New York Times, July 1, 2010). Assume 150 patients decide to get their genome sequenced. a. If the claim by scientists is accurate, what is
American workers are increasingly planning to delay retirement (US News & World Report, June 30, 2010). According to a Pew Research Center comprehensive survey, 35% of employed adults of age 62 and older say they have pushed back their retirement date.a. What is the probability that in a sample
Presidential job approval is the most-watched statistic in American politics. According to the June 2010 NBC/ Wall Street Journal public opinion poll, president Barack Obama had reached his lowest approval rating since taking office in January of 2009. The poll showed that 48% of people disapproved
The producer of a particular brand of soup claims that its sodium content is 50% less than that of its competitor.The food label states that the sodium content measures 410 milligrams per serving. Assume the population of sodium content is normally distributed with a standard deviation of 25
A variety of packaging solutions exist for products that must be kept within a specific temperature range.Cold chain distribution is particularly useful in the food and pharmaceutical findustries. A packaging company strives to maintain a constant temperature for its packages. It is believed that
Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 10% of produced items are known to be nonconforming. Every week a batch of items is evaluated
In the previous question, suppose that the management decides to use a p chart for the analysis. As noted earlier, 10% of produced items are known to be nonconforming.The firm analyzes a batch of production items for 6 weeks and computes the following percentages of nonconforming items.Week
Forty families gathered for a fund-raising event. Suppose the find ividual contribution for each family is normally distributed with a mean and a standard deviation of $115 and $35, respectively. The organizers would call this event a success if the total contributions exceed $5,000. What is the
The significant decline of savings in the United States from the 1970s and 1980s to the 1990s and 2000s has been widely discussed by economists (money.cnn.com, June 30, 2010). According to the Bureau of Economic Analysis, the savings rate of American house holds, defined as a percentage of the
According to a report, college graduates in 2010 were likely to face better job prospects than 2009 graduates (New York Times, May 24, 2010). Many employers who might have been pessimistic at the start of the 2009-2010 academic year were making more offers than expected. Despite the improvement in
Hockey pucks used by the National Hockey League (NHL) and other professional leagues weigh an average of 163 grams (5.75 ounces). A quality inspector monitors the manufacturing process for hockey pucks. She takes eight samples of n=10. Measured in grams, the weights appear in the table below. It is
Find zα/2 for each of the following confidence levels used in estimating the population mean.a. 90%b. 98%c. 88%
Find zα/2 for each of the following confidence levels used in estimating the population mean.a. 89%b. 92%c. 96%
A simple random sample of 25 observations is derived from a normally distributed population with a known standard deviation of 8.2.a. Is the condition that is normally distributed satisfied? Explain.b. Compute the margin of error with 80% confidence.c. Compute the margin of error with 90%
Consider a population with a known standard deviation of 26.8. In order to compute an interval estimate for the population mean, a sample of 64 observations is drawn.a. Is the condition that is normally distributed satisfied? Explain.b. Compute the margin of error at a 95% confidence level.c.
Discuss the factors that influence the margin of error of the confidence interval for the population mean. What can a practitioner do to reduce the margin of error?
The average life expectancy for Bostonians is 78.1 years (The Boston Globe, August 16, 2010). Assume that this average was based on a sample of 50 Bostonians and that the population standard deviation is 4.5 years.a. What is the point estimate of the population mean?b. At 90% confidence, what is
In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 28 recent loans is taken. The average calculated from this sample is 5.25%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of
An article in the National Geographic News (“U.S. Racking Up Huge Sleep Debt,” February 24, 2005) argues that Americans are increasingly skimping on their sleep. A researcher in a small mid-western town wants to estimate the mean weekday sleep time of its adult residents. He takes a random
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