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mathematics
statistics

Questions and Answers of Statistics

The U.S. Department of Transportation maintains statistics for involuntary denial of boarding. In May 2012, the American Airlines rate of involuntarily denying boarding was 0.81 per 10,000
Based on past experience, it is assumed that the number of flaws per foot in rolls of grade 2 wallpaper follows a Poisson distribution with a mean of 1 flaw per 5 feet of wallpaper (i.e., 0.2 flaw
J.D. Power and Associates calculates and publishes various statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For 2012 model cars, Ford had
If you purchased a 2012 Toyota, what is the probability that the new car will havea. Zero problems?b. Two or fewer problems?c. Compare your answers in (a) and (b) to those for the 2012 Ford in
Another article reported that in 2011, Ford had 1.16 problems per car and Toyota had 1.01 problems per car. (Data extracted from M. Ramsey, "Ford Drops in Quality Survey," The Wall Street Journal,
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that
If you purchased a 2011 Toyota, what is the probability that the new car will havea. Zero problems?b. Two or fewer problems?c. Compare your answers in (a) and (b) to those for the 2012 Toyota in
A toll-free phone number is available from 9 A.M. to 9 P.M. for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 0.8 calls
Determine the following:a. If n = 4, N = 10, and A = 5, find P(X = 3).b. If n = 4, N = 6, and A = 3, find P(X = 1).c. If n = 5, N = 12, and A = 3, find P{X = 0).d. If n = 3, N = 10, and A = 3, find
Compute the mean and standard deviation for the hypergeometric distributions described in (a) through (d).For Information: Referring to Problem 5.42
An auditor for the Internal Revenue Service is selecting a sample of 6 tax returns for an audit. If 2 or more of these returns are "improper," the entire population of 100 tax returns will be
KSDLDS-Pros, an IT project management consulting firm, is forming an IT project management team of 5 professionals. In the firm of 50 professionals, 8 are considered to be data analytics specialists.
From an inventory of 30 cars being shipped to a local automobile dealer, 4 are SUVs. What is the probability that if 4 cars arrive at a particular dealership,a. All 4 are SUVs?b. None are SUVs?c. At
As a quality control manager, you are responsible for checking the quality level of AC adapters for tablet PCs that your company manufactures. You must reject a shipment if you find 4 defective
A financial analyst was facing the task of selecting mutual funds to purchase for a client's portfolio. Suppose that the number of funds had been narrowed to 12 funds instead of the 10 funds (still
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the following results:a. Compute the expected
What are the four properties that must be present in order to use the binomial distribution? Discuss in detail.
What are the four properties that must be present in order to use the Poisson distribution? Discuss in detail.
When do you use the hypergeometric distribution instead of the binomial distribution? Discuss.
Darwin Head, a 35-year-old sawmill worker, won $l million and a Chevrolet Malibu Hybrid by scoring 15 goals within 24 seconds at the Vancouver Canucks National Hockey League game (B. Ziemer, "Darwin
Between 1896 when the Dow Jones Index was created and 2009, the index rose in 64% of the years. (Data extracted from M. Hulbert, "What the Past Can't Tell Investors," The New York Times, January 3,
In early 2012, it was reported that 38% of U.S. adult cell phone owners called a friend for advice about a purchase while in a store. (Data extracted from "Mobile Advice, Sunday Stats" The Palm Beach
One theory concerning the Dow Jones Industrial Average is that it is likely to increase during U.S. presidential election years. From 1964 through 2008, the Dow Jones Industrial Average increased in
Medical billing errors and fraud are on the rise. According to Medical Billing Advocates of America, 8 out of 10 times, the medical bills that you get are not right. (Data extracted from "Services
Suppose that a quality improvement initiative has reduced the percentage of medical bills containing errors to 40%. If a sample of 10 medical bills is selected, what is the probability thata. 0
Social log-ins involve recommending or sharing an article that you read online. According to Janrain ("T. Wayne, One Log-In Catches on for Many Sites," The New York Times, May 2, 2011, p. B2), in the
The manager of the commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these
One of the biggest frustrations for the consumer electronics industry is that customers are accustomed to returning goods for any reason (C. Lawton, "The War on Returns," The Wall Street Journal, May
In the same time period, 27% of the returns were for "buyer's remorse."a. What is the expected value, or mean, of the binomial distribution?b. What is the standard deviation of the binomial
One theory concerning the S&P 500 Index is that if it increases during the first five trading days of the year, it is likely to increase during the entire year. From 1950 through 2010, the
Spurious correlation refers to the apparent relationship between variables that either have no true relationship or are related to other variables that have not been measured. One widely publicized
In a recent year, it was reported that approximately 300 million golf balls were lost in the United States. Assume that the number of golf balls lost in an 18-hole round is distributed as a Poisson
In the Florida lottery Lotto game, you select six numbers from a pool of numbers from 1 to 53 (see flalottery.com). Each wager costs $1. You win the jackpot if you match all six numbers that you have
Given the following probability distributions for variables X and Y:Computea. E(X) and E(F).b. Ïƒx and Ïƒy.c. ÏƒXY.d. E(X + Y).
Given the following probability distributions for variables X and Y:Computea. E(X) and E(Y).b. ÏƒX and ÏƒY.c. aXY.d. E(X + Y).
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability thata. Zis less than 1.57?b. Zis greater than 1.84?c. Zis between
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8.a. What is the probability that a student scored below
A Nielsen study indicates that mobile subscribers between 18 and 24 years of age spend a substantial amount of time watching video on their devices, reporting a mean of 325 minutes per month. (Data
In 2011, the per capita consumption of coffee in Sweden was reported to be 7.27 kg, or 15.994 pounds. (Data extracted from www.ico.org.) Assume that the per capita consumption of coffee in Sweden in
Many manufacturing problems involve the matching of machine parts, such as shafts that fit into a valve hole. A particular design requires a shaft with a diameter of 22.000 mm, but shafts with
Show that for a sample of n = 39, the smallest and largest Z values are -1.96 and +1.96, and the middle (i.e., 20th) Z value is 0.00.
For a sample of n = 6, list the six Z values. Discuss.
The file RIP1 contains the overall miles per gallon (MPG) of 2012 small SUVs (n = 18):Decide whether the data appear to be approximately normally distributed bya. Comparing data characteristics to
As player salaries have increased, the cost of attending baseball games has increased dramatically. The file BBcost2011 contains the cost of lour tickets, two beers, four soft drinks, four hot dogs,
The file Property Taxes contains the property taxes per capita for the 50 states and the District of Columbia. Decide whether the data appear to be approximately normally distributed bya. Comparing
Thirty companies comprise the DJIA. How big are these companies? One common method for measuring the size of a company is to use its market capitalization, which is computed by multiplying the number
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability thata. Zis between-1.57 and 1.84?b. Z is less than-1.57 or greater
One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in an automotive plant. The steel is cut with a diamond saw, and the resulting parts
The file contains the yields for a one-year certificate of deposit (CD) and a five-year CD for 24 banks in the United States, as of June 21, 2012. (Data extracted from www.Bankrate.com, June 21,
The file Utility contains the electricity costs, in dollars, during July 2012 for a random sample of 50 one-bedroom apartments in a large city:Decide whether the data appear to be approximately
Suppose you select one value from a uniform distribution with a = 0 and b = 10. What is the probability that the value will be a. Between 5 and 7? b. Between 2 and 3? c. What is the mean? d. What is
The time between arrivals of customers at a bank during the noon-to-1 P.M. hour has a uniform distribution between 0 to 120 seconds. What is the probability that the time between the arrival of two
A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an approximately uniform distribution between 20 minutes and 40 minutes. What is the probability
How long does it take to download a game for your iPod? According to Apple's technical support site, support.apple.com/kb/htl577, downloading an iPod game using a 5 Mbit/s broadband connection should
The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. What
Given an exponential distribution with A = 10, what is the probability that the arrival time isa. Less than X = 0.1?b. Greater than X = 0.1?c. Between X = 0.1 and X = 0.2?d. Less than X = 0.1 or
Given an exponential distribution with A = 30, what is the probability that the arrival time isa. Less than X = 0.1?b. Greater than X = 0.1?c. Between X = 0.1 and X = 0.2?d. Less than X = 0.1 or
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability thata. Zis less than 1.08?b. Zis greater than-0.21?c. Z is less
Given an exponential distribution with A = 5, what is the probability that the arrival time isa. Less than X = 0.3?b. Greater than X = 0.3?c. Between X = 0.3 and X = 0.5?d. Less than X = 0.3 or
Autos arrive at a toll plaza located at the entrance to a bridge at a rate of 50 per minute during the 5:00-to-6:00 p.m. hour. If an auto has just arrived,a. what is the probability that the next
Customers arrive at the drive-up window fast-food restaurant at a rate of 2 per minute c the lunch hour.a. What is the probability that the next customer will within 1 minute?b. What is the
Telephone calls arrive at the information desk large computer software company at a rate of 15 per hia. What is the probability that the next call will a within 3 minutes (0.05 hour)?b. What is the
An on-the-job injury occurs once every 10 da; average at an automobile plant. What is the probability the next on-the-job injury will occur withina. 10 days?b. 5 days?c. 1 day?
The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 20 days. Find the probability that the time between two unplanned shutdowns isa. Less than 14
Golfers arrive at the starter's booth of a public golf course at a rate of 8 per hour during the Monday-to-Friday midweek period. If a golfer has just arrived,a. what is the probability that the next
Some Internet companies sell a service that will boost a website's traffic by delivering additional unique visitors. Assume that one such company claims it can deliver 1,000 visitors a day. If this
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), determine the following probabilities:a. P(Z > 1.08)b. P(Z < -0.21)c. P(-1.96 < Z
What are some of the distinguishing properties of a normal distribution? Discuss in detail.
How does the shape of the normal distribution differ from the shapes of the uniform and exponential distributions? Discuss in detail.
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearings can operate are 0.74 inch and
The fill amount in 2-liter soft drink bottles is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If bottles contain less than 95% of the listed net content
In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler in Problem 6.46 sets the filling machine so that the mean is 2.02 liters. Under these circumstances, what
An orange juice producer buys all his oranges from a large orange grove. The amount of juice squeezed from each of these oranges is approximately normally distributed, with a mean of 4.70 ounces and
The file contains the percentage alcohol, number of calories per 12 ounces, and number of carbohydrates (in grams) per 12 ounces for 150 of the best-selling domestic beers in the United States. For
Given a normal distribution with μ = 100 and σ = 10, what is the probability thata. X > 75?b. X < 70?c. X < 80 or X >110?d. Between what two X values (symmetrically distributed around
The evening manager of a restaurant was very concerned about the length of time some customers were waiting in line to be seated. She also had some concern about the seating times-that is, the length
The major stock market indexes had mixed results in 2011. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was 0.00%. The mean one-year return for the NASDAQ,
The speed at which you can log into a website through a smart phone is an important quality characteristic of that website. In a recent test, the mean time to log into the JetBlue Airways website
The speed at which you can log into a website through a smart phone is an important quality characteristic of that website. In a recent test, the mean time to log into the Hertz website through a
Given a normal distribution with μ = 50 and σ = 4, what is the probability thata. X > 43?b. X< 42?c. 5% of the values are less than what X value?d. Between what two X values (symmetrically
In 2011, the per capita consumption of coffee in the United States was reported to be 4.16 kg, or 9.152 pounds. (Data extracted from www.ico.org.) Assume that the per capita consumption of coffee in
Toby's Trucking Company determined that the distance traveled per truck per year is normally distributed, with a mean of 50 thousand miles and a standard deviation of 12 thousand miles.a. What
Consumers spend an average of $21 per week in cash without being aware of where it goes. (Data extracted from "A Hole in Our Pockets," USA Today, January 18, 2010, p. 1 A.) Assume that the amount of
Given a normal distribution with /x = 100 and cr = 10, if you select a sample of n = 25, what is the probability that Zisa. Less than 95?b. Between 95 and 97.5?c. Above 102.2?d. There is a 65% chance
A random sample of 50 households was selected for a phone (landline and cell phone) survey. The key question asked was, "Do you or any member of your household own an Apple product (iPhone, iPod,
The following data represent the responses (Y for yes and N for no) from a sample of 40 college students to the question "Do you currently own shares in any stocks?"NNYNNYNYNYNNYNYYNNNY
A political pollster is conducting an analysis HS9 of sample results in order to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least 55%
You plan to conduct a marketing experiment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample
In a recent survey of full-time female workers ages 22 to 35 years, 46% said that they would rather give up some of their salary for more personal time. (Data extracted from "I'd Rather Give Up," USA
UK-based Chartered Institute of Management Accountants (CIMA) reports that 57% of its member organizations provide training on ethical standards at work. (Data extracted from bit.ly/Mlt08H.) Suppose
A survey of 2,250 American adults reported that 59% got news both online and offline in a typical day. (Data extracted from "How Americans Get News in a Typical Day," USA Today, March 10, 2010, p.
Given a normal distribution with JX - 50 and a = 5, if you select a sample of n = 100, what is the probability that X isa. Less than 47?b. Between 47 and 49.5?c. Above 51.1?d. There is a 35% chance
Why does the standard error of the mean decrease as the sample size, n, increase?
Why does the sampling distribution of the mean follow a normal distribution for a large enough sample size, even though the population may not be normally distributed? Discuss in detail.
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearing can operate are 0.74 inch
The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If you select a random sample of 25 bottles, what is the
An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of
In Problem 7.26, suppose that the mean amount of juice squeezed is 5.0 ounces.a. What is the probability that the sample mean amount of juice will be at least 4.60 ounces?b. The probability is 70%
The stock market in Mexico reported weak returns in 2011. The population of stocks earned a mean return of -3.8% in 2011. (Data extracted from USA Today, January 3, 2012, p. 2B.) Assume that the
If you select an individual stock from this population, what is the probability that it would have a return.a. Less than 0 (i.e., a loss)?b. Between -10 and -20?c. Greater than -5?If you selected a

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