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statistics

Questions and Answers of Statistics

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).
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
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,
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
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
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
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
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
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
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
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
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
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,
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 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
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
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
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
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
Body mass index (BMI) is a reliable indicator of body fat for most children and teens. BMI is calculated from a childâ€™s weight and height and is used as an easy-to-perform method of screening
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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.
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
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
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
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
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
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
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
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,
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?
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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,
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
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.
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
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
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
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
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
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
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.
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
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.
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
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
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
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
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
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?
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
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
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
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

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