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mathematics
statistics

Questions and Answers of Statistics

Compute the number of ways you can select n elements from N elements for each of the following: a. n = 2, N = 5 b. n = 3, N = 6 c. n = 5, N = 20
For two events, A and B, P(A) = .4, P(B) = .2, and P(A | B) = .6: a. Find P(A ∩ B). b. Find P(B | A).
For two independent events, A and B, P(A) = .4 and P(B) = .2: a. Find P(A ∩ B) b. Find P(A | B). c. Find P(A ⋃ B)
Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the following probabilities: P(E1 = .20, P(E2) = .30, P(E3)
Two fair coins are tossed, and the following events are defined:A: {Observe at least one head}B: {Observe exactly one head}a. Draw a Venn diagram for the experiment, showing events A and B. Assign
Two fair dice are tossed, and the following events are defined: A: {Sum of the numbers showing is odd} B: {Sum of the numbers showing is 9, 11, or 12} Are events A and B independent? Why?
Human Performance (Vol. 23, 2010) published the results of a study that found that arrogant workers are more likely to have poor performance ratings. Suppose that 15% of all full-time workers exhibit
Forbes (Apr. 20, 2011) conducted a survey of the 20 largest public companies in the world. Of these 20 companies, 4 were banking or investment companies based in the United States. A total of 9 U.S.
Two fair dice are tossed, and the face on each die is observed. a. Use a tree diagram to find the 36 sample points contained in the sample space. b. Assign probabilities to the sample points in part
According to The National Crime Victimization Survey (December 2010), published by the U.S. Department of Justice, about 11.7 million people were victims of identity theft over the past 2 years. This
Refer to the Journal of Allied Health (Fall 2011) study of why emergency medical service (EMS) workers leave the profession, Exercise 3.41. Recall that in a sample of 244 former EMS workers, 127 were
Refer to the Adweek/Harris (July 2011) poll of whether U.S. adults work during their summer vacation, Exercise 3.14. Recall that the poll found that 46% of the respondents work during their summer
The summary table giving the number of the 158,044 Finnish citizens in each IQ score/investment category is reproduced below. Again, suppose one of the citizens is selected at random.For Information:
Survey of the top 40 best-paid CEOs shown in Table 2.1. The data on highest degree obtained are summarized in the SPSS printout below.For Information: Refer to the results of the Forbes (April 13,
Geographical Analysis (Jan. 2010) presented a study of emergency medical service (EMS) ability to meet the demand for an ambulance. In one example, the researchers presented the following scenario.
The U.S. Census Bureau reports a decline in the percentage of mothers in the workforce who have infant children. The following table gives a breakdown of the marital status and working status of the
Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles. a. List the sample points for this experiment. b. Assign probabilities to the
The Journal of Wine Research (Vol. 21, 2010) published a study of the effects of soil and climate on the quality of wine produced in Spain. The soil at two vineyards-Llarga and Solar-was the focus of
Red snapper is a rare and expensive reef fish served at upscale restaurants. Federal law prohibits restaurants from serving a cheaper, look-alike variety of fish (e.g., vermillion snapper or lane
The software for a lie detector based on voice stress levels - called the computerized voice stress analyzer (CVSA) - is available for about $10,000. The manufacturer claims that the CVSA is 98%
Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects.
In Parade Magazine's (Nov. 26, 2000) column "Ask Marilyn," the following question was posed: "I have just tossed a [balanced] coin 10 times, and I ask you to guess which of the following three
Portions of computer software code that may contain undetected defects are called blind spots. The issue of blind spots in software code evaluation was addressed at the 8th IEEE International
Suppose the events B1 and B2 are mutually exclusive and complementary events, such that P(B1) = .75 and P(B2) = .25. Consider another event A such that P(A|B1) = .3 and P(A|B2) = .5. a. Find P(B1 ∩
Suppose the events B1, B2, and B3 are mutually exclusive and complementary events, such that P(B1) = .2, P(B2) = .15, and P(B3) = .65. Consider another event A such that P(A) = .4. If A is
Currently, there are three diagnostic tests available for chromosome abnormalities in a developing fetus: triple serum marker screening, ultrasound, and amniocentesis. The safest (to both the mother
Contrary to what is presented on TV shows like CSI, fingerprint identification is not fully automated. Expert examiners are required to identify the person who left the fingerprint. A study published
A construction company employs three sales engineers. Engineers 1, 2, and 3 estimate the costs of 30%, 20%, and 50%, respectively, of all jobs bid by the company. For i = 1, 2, 3, define Ei to be the
Due to inaccuracies in drug-testing procedures (e.g., false positives and false negatives) in the medical field, the results of a drug test represent only one factor in a physician's diagnosis. Yet,
Dolomite is a valuable mineral that is found in sedimentary rock. During mining operations, dolomite is often confused with shale. The radioactivity features of rock can aid miners in distinguishing
An important component of your desktop or laptop personal computer (PC) is a microchip. The table gives the proportions of microchips that a certain PC manufacturer purchases from seven suppliers.a.
Recall that if there is an intruder, system A sounds an alarm with probability .9, and system B sounds an alarm with probability .95. If there is no intruder, system A sounds an alarm with
Following the assassination of President John F. Kennedy (JFK) in 1963, the House Select Committee on Assassinations (HSCA) conducted an official government investigation. The HSCA concluded that
In 1940, Forrest E. Mars Sr. formed the Mars Corporation to produce chocolate candies with a sugar shell that could be sold throughout the year and wouldn't melt during the summer. Originally, M&M's
Which of the following describe continuous random variables? Which describe discrete random variables? a. The number of newspapers sold by the New York Times each month b. The amount of ink used in
Financial analysts who make forecasts of stock prices are categorized as either "buy-side" analysts or "sell-side" analysts. Refer to the Financial Analysts Journal (Jul./Aug. 2008) comparison of
One of the CRASH variables saved in the accompanying file is the severity of a driver's head injury when the car is in a head-on collision with a fixed barrier while traveling at 35 miles per hour.
In Exercise 4.49 you learned that half of all U.S. adults use the Internet and have paid to download music (Pew Internet & American Life Project Survey, October 2010). In a random sample of 250 U.S.
According to studies, 1 % of all patients who undergo laser surgery (i.e., LASIK) to correct their vision have serious post laser vision problems (All About Vision, 2012). In a sample of 100,000
Six Sigma is a comprehensive approach to quality goal setting that involves statistics. An article in Aircraft Engineering and Aerospace Technology (Vol. 76, No. 6, 2004) demonstrated the use of the
Ambulance response time is measured as the time (in minutes) between the initial call to emergency medical services (EMS) and when the patient is reached by ambulance. Geographical Analysis (Vol. 41,
Personnel tests are designed to test a job applicant's cognitive and/or physical abilities. The Wonderlic IQ test is an example of the former; the Purdue Pegboard speed test involving the arrangement
A discrete random variable x can assume five possible values: 20, 21, 22, 23, and 24. The following Minitab histogram shows the likelihood of each value.a. What is p(22)?b. What is the probability
Government data indicate that the mean hourly wage for manufacturing workers in the United States is $18.50 (Statistical Abstract of the United States: 2012). Suppose the distribution of
During a presidential election, each state is allotted a different number of votes in the Electoral College depending on population. For example, California is allotted 55 votes (the most) while
The probability of a hotel guest participating in the hotel's "green" conservation program by reusing towels and bed linens is .45. Suppose a large hotel chain randomly samples 200 of its guests. The
The following table reports the U.S. credit card industry's market share data for 2011. A random sample of 100 credit card users is to be questioned regarding their satisfaction with their credit
Poor executive leadership during business meetings can result in counterproductive outcomes (e.g., negative employee attitudes, ambiguous objectives). Can executive coaching help improve business
What relationship exists between the standard normal distribution and the box-plot methodology (Section 2.8) for describing distributions of data using quartiles? The answer depends on the true
If a population data set is normally distributed, what is the proportion of measurements you would expect to fall within the following intervals? a. μ ± σ b. μ ± 2σ c. μ ± 3σ
Normal probability plots for three data sets are shown below. Which plot indicates that the data are approximately normally distributed?
The random variable x has the following discrete probability distribution:a. List the values x may assume.b. What value of x is most probable?c. Display the probability distribution as a
Examine the sample data in the accompanying table.a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution.b. Compute 5 for the sample data.c. Find
Data on the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) for each of 992 senior managers at CPA firms are saved in the accompanying
Software configuration management was used to monitor a software engineering team's performance at Motorola, Inc. (Software Quality Professional, Nov. 2004). One of the variables of interest was the
Wear-out failure time of electronic components is often assumed to have a normal distribution. Can the normal distribution be applied to the wear-out of used manufactured products, such as colored
Refer to the NHTSA crash test data for new cars. In Exercise 4.102, you assumed that the driver's head-injury rating is approximately normally distributed. Apply the methods of this chapter to the
Refer to the data on the Dec. 2008 sanitation scores for 186 cruise ships, first presented in Exercise 2.24. The data are saved in the accompanying file. Assess whether the sanitation scores are
Recall that the method incorporates a golfer's average driving distance (yards) and driving accuracy (percent of drives that land in the fairway) into a driving performance index. Data on these three
A discrete random variable x can assume five possible values: 2, 3, 5, 8, and 10. Its probability distribution is shown here:a. What is p(5)?b. What is the probability that x equals 2 or 10?c. What
The DoD RAC publishes START sheets for government and industry. These START sheets are designed to improve the reliability, maintainability, supportability, and quality of manufactured components and
The variable of interest is the total semester hours of college credit for each candidate. Recall that the mean and median for the data set were 141.31 and 140 hours, respectively, and the standard
Suppose x is a random variable best described by a uniform probability distribution with c = 3 and d = 7.a. Find f(x).b. Find the mean and standard deviation of x.c. Find P(μ - σ ≤ x ≤ μ + σ).
Suppose x is a random variable best described by a uniform probability distribution with c = 20 and d = 45. a. Find f(x). b. Find the mean and standard deviation of x. c. Graph f(x) and locate μ and
Refer to Exercise 4.133. Find the following probabilities:a. P(20 ≤ x ≤ 30)b. P(20 < x ≤ 30)c. P(x ≥ 30)d. P(x ≥ 45)e. P(x ≤ 40)f. P(x < 40)g. P(15 ≤ x ≤ 35)h. P(21.5 ≤ x ≤
Suppose x has an exponential distribution with  = 1. Find the following probabilities:a. P(x > 1)b. P(x ≤ 3)c. P(x > 1.5)d. P(x ≤ 5)
The random variable x is best described by a uniform probability distribution with c = 100 and d = 200. Find the probability that x assumes a valuea. More than 2 standard deviations from μ.b. Less
Explain why each of the following is or is not a valid probability distribution for a discrete random variable x:a.b.c.d.
Maintaining a constant pipe wall temperature in some hot-process applications is critical. A technique that utilizes bolt-on trace elements to maintain temperature was presented in the Journal of
Researchers at the University of South Florida Center for Biological Defense have developed a safe method for rapidly detecting anthrax spores in powders and on surfaces (USF Magazine, Summer 2002).
On the basis of data collected from metal shredders across the nation, the amount x of extractable lead in metal shredder residue has an approximate exponential distribution with mean θ = 2.5
Social networking sites for business professionals are used to promote one's business. Each social network involves interactions (connections) between members of the network. Researchers define
The frequency distribution shown in the next table depicts the property and marine losses incurred by a large oil company over the last 2 years. This distribution can be used by the company to
The manager of a local soft-drink bottling company believes that when a new beverage-dispensing machine is set to dispense 7 ounces, it in fact] dispenses an amount x at random anywhere between 65
Refer to the Chance (Summer 2007) article on phishing attacks at a company, Exercise 2.33. Recall that phishing describes an attempt to extract personal/financial information through fraudulent
An article in Hotwire (Dec. 2002) discussed the length of time till failure of a product produced at Hewlett-Packard. At the end of the product's lifetime, the time till failure is modeled using an
A die is tossed. Let x be the number of spots observed on the upturned face of the die. a. Find the probability distribution of x and display it in tabular form. b. Display the probability
In the jargon of system maintenance, cycle availability is defined as the probability that the system is functioning at any point in time. The DoD developed a series of performance measures for
A tool-and-die machine shop produces extremely high-tolerance spindles. The spindles are 18-inch slender rods used in a variety of military equipment. A piece of equipment used in the manufacture of
For a certain type of halogen light bulb, an old bulb that has been in use for a while tends to have a longer life than a new bulb. Let x represent the life (in hours) of a new halogen light bulb and
Toss three fair coins and let x equal the number of heads observed.a. Identify the sample points associated with this experiment and assign a value of x to each sample point.b. Calculate p(x) for
Consider the probability distributions shown here:a. Use your intuition to find the mean for each distribution. How did you arrive at your choice?b. Which distribution appears to be more variable?
Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are
According to Nielsen's Television Audience Report, 2010 & 2011, 26% of all U.S. TV house-holds have a size of 1 person, 32% have a household size of 2,17% have a household size of 3, and 25% have
A summary of the CRASH driver-side star ratings for the 98 cars in the file is reproduced in the accompanying Minitab printout. Assume that one of the 98 cars is selected at random and let x equal
The age distribution for the employees of a highly successful "dot-com" company headquartered in Atlanta is shown in the next table. An employee is to be randomly selected from this population.a. Can
According to an August 2011 survey by the Pew Internet & American Life Project, nearly 40% of adult cell phone owners have downloaded an application ("app") to their cell phone. The next table
Recall that each of 124 college students selected showroom displays for portable grills. Five different displays (representing five different-sized grills) were available, but the students were
Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and
In an effort to minimize the monetary losses that result from a devastating Florida hurricane, part of the researchers' analysis included a graphic showing the sequence number of tropical storms
Consider a random sample of three slaughtered chickens that all pass USDA inspection. Let x equal the number of chickens in the sample that have fecal contamination.a. Find p(x) for x = 0, 1, 2, 3.b.
A weapons manufacturer uses a liquid propellant to produce gun cartridges. During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A
he Journal of Consumer Research (August 2011) published a study demonstrating the "last name" effect-i.e., the tendency for consumers with last names that begin with a later letter of the alphabet to
During autumn 2001, there was a highly publicized outbreak of anthrax cases among U.S. Postal Service workers. In Chance (Spring 2002), research statisticians discussed the problem of sampling
The risk of a portfolio of financial assets is sometimes called investment risk. In general, investment risk is typically measured by computing the variance or standard deviation of the probability
Recall that an IQ score (from a low score of 1 to a high score of 9) was determined for each in a sample of 158,044 Finnish citizens. Also recorded was whether or not the citizen invested in the
The National Weather Service issues precipitation forecasts that indicate the likelihood of measurable precipitation (≥ .01 inch) at a specific point (the official rain gauge) during a given time
Most states offer weekly lotteries to generate revenue for the state. Despite the long odds of winning, residents continue to gamble on the lottery each week. In SIA, Chapter 3, you learned that the
Engineers at Broadcom Corp. and Simon Fraser University collaborated on research involving a robot-sensor system in an unknown environment (International Journal of Robotics Research, Dec. 2004). As
Odds makers try to predict which professional and college football teams will win and by how much (the spread). If the odds makers do this accurately, adding the spread to the underdog's score should

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