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statistics

Questions and Answers of Statistics

The number of customers, x, waiting in line to order sandwiches at a Subway shop at noon is of interest to the store manager. What values can x assume? Is x a discrete or continuous random variable?
Compute the following:a. 6! / 2! (6 - 2)!b.c.d.e.
Consider the following probability distribution:a. Is x a discrete or a continuous random variable?b. What is the name of this probability distribution?c. Graph the probability distribution.d. Find
If x is a binomial random variable, compute p(x) for each of the following cases: a. n = 5, x = 1, p = .2 b. n = 4, x = 2, q = .4 c. n = 3, x = 0, p = .7 d. n = 5, x = 3, p = .1 e. n = 4, x = 2, q =
If x is a binomial random variable, use Table I in Appendix D to find the following probabilities:a. P(x = 2) for n = 10, p = .4b. P(x ≤ 5) for n = 15, p = .6c. P(x > l) for n = 5, p = .1d. P(x
If x is a binomial random variable, calculate μ, σ2, and σ for each of the following: a. n = 25, p = .5 b. n = 80, p = .2 c. n = 100, p = .6 d. n = 70, p = .9 e. n = 60, p = .8 f. n = 1,000, p =
The binomial probability distribution is a family of probability distributions with each single distribution depending on the values of n and p. Assume that x is a binomial random variable with n =
Adweek/Harris (July 2011) poll found that 35% of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let x represent the number who do not work during
Each year, J.D. Power and Associates publishes the results of its North American Hotel Guest Satisfaction Index Study. For 2009, the study revealed that 66% of hotel guests were aware of the hotel's
A Pew Internet & American Life Project Survey (October 2010) revealed that half of all U.S. adults use the Internet and have paid to download music. In a random sample of 250 U.S. adults, let x be
Many primary care doctors feel overworked and burdened by potential lawsuits. In fact, the Physicians' Foundation reported that 60% of all general practice physicians in the United States do not
According to the Canadian Journal of Information and Library Science (Vol. 33, 2009), nearly 90% of workers in law libraries are satisfied with their job. Assume the true proportion of law librarians
The study found that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. In contrast, a novice will correctly identify the
Recall the scenario where you are one of five county commissioners voting on an issue, and each commissioner is equally likely to vote for or against. a. Your vote counts (i.e., is the decisive vote)
According to the National Bridge Inspection Standard (NBIS), public bridges over 20 feet in length must be inspected and rated every 2 years. The NBIS rating scale ranges from 0 (poorest rating) to 9
According to the Internal Revenue Service (IRS), the chances of your tax return being audited are about 1 in 100 if your income is less than $1 million and 9 in 100 if your income is $1 million or
Every quarter, the Food and Drug Administration (FDA) produces a report called the Total Diet Study. The FDA's report covers a variety of food items, each of which is analyzed for potentially harmful
Suppose you are a purchasing officer for a large company. You have purchased 5 million electrical switches, and your supplier has guaranteed that the shipment will contain no more than .1%
According to the U.S. Golf Association (USGA), "The weight of the [golf] ball shall not be greater than 1.620 ounces avoirdupois (45.93 grams). The diameter of the ball shall not be less than 1.680
Consider the probability distribution shown here:a. Is x a discrete or continuous random variable? Explain.b. What is the name of this probability distribution?c. Graph the probability
Assume that x is a random variable having a Poisson probability distribution with a mean of 1.5. Use statistical software to find the following probabilities:a. P(x ≤ 3)b. P(x ≥ 3)c. P(x = 3)d.
Given that x is a hyper geometric random variable, compute p(x) for each of the following cases: a. N = 5, n = 3, r = 3, x = 1 b. N = 9, n = 5, r = 3, x = 3 c. N = 4, n = 2, r = 2, x = 2 d. N = 4, n
Given that x is a random variable for which a Poisson probability distribution provides a good approximation, use statistical software to find the following:a. P(x ≤ 2) when  = 1b. P(x ≤ 2)
Suppose x is a random variable for which a Poisson probability distribution with  = 5 provides a good characterization.a. Graph p(x) for x = 0, 1, 2,..., 15.b. Find μ and σ for x and locate μ
Suppose you plan to sample 10 items from a population of 100 items and would like to determine the probability of observing 4 defective items in the sample. Which probability distribution should you
The study found that of 106 social robots, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. Suppose you randomly select 10 of the
The Federal Deposit Insurance Corporation (FDIC) normally insures deposits of up to $100,000 in banks that are members of the Federal Reserve System against losses due to bank failure or theft. Over
U.S. airlines average about 4.5 fatalities per month (Statistical Abstract of the United States: 2012). Assume the probability distribution for x, the number of fatalities per month, can be
According to the International Nanny Association (INA), 4,176 nannies were placed in a job during a recent year (www.nanny.org). Of these, only 24 were men. In Exercise 3.11 you found the probability
In a sample of 158 cartridges from a certain lot, 36 were found to be contaminated and 122 were "clean." If you randomly select 5 of these 158 cartridges, what is the probability that all 5 will be
A "planet transit" is a rare celestial event in which a planet appears to cross in front of its star as seen from Earth. The planet transit causes a noticeable dip in the star's brightness, allowing
Recall that the managers of 30 leading museums of contemporary art were asked to provide the performance measure used most often. Of these 30 museums, 8 specified "total visitors" as the performance
The relationship between close sporting events and game-day traffic fatalities was investigated in the Journal of Consumer Research (December 2011). The researchers found that closer football and
An automatic car wash takes exactly 5 minutes to wash a car. On average, 10 cars per hour arrive at the car wash. Suppose that 30 minutes before closing time, 5 cars are in line. If the car wash is
Find the area under the standard normal probability distribution between the following pairs of z-scores: a. z = 0 and z = 2.00 b. z = 0 and z = 3 c. z = 0 and z = 1.5 d. z = 0 and z = .80
Find the following probabilities for the standard normal random variable z:a. P(z > 1.46)b. P(z < -1.56)c. P(.67 ≤ z < 2.41)d. P(-1.96 ≤ z < -.33)e. P(z ≥ 0)f. P(-2.33 < z <
Find the following probabilities for the standard normal random variable z:a. P(-l < z < 1)b. P(-2 < z < 2)c. P(-2.16 ≤ z ≤ .55)d. P(-.42 < z < 1.96)e. P(z ≥ -2.33)f. P(z <
Find each of the following probabilities for the standard normal random variable z:a. P(-l ≤ z ≤ 1)b. P(-1.96 ≤ z ≤ 1.96)c. P(-1.645 ≤ z ≤ 1.645)d. P(-2 ≤ z ≤ 2)
Find a value of the standard normal random variable z, call it z0, such thata. P(z ≥ z0) = .05b. P(z ≥ z0) = .025c. P(z ≤ z0) = .025d. P(z ≤ z0) = .10e. P(z > z0) = .10
Find a value of the standard normal random variable z, call it z0, such thata. P(z ≤ z0) = .2090b. P(z ≤ z0) = .7090c. P(-z0 ≤ z < Z0) = .8472d. P(-z0 ≤ z < z0) = .1664e. P(z0 ≤ z ≤
Give two examples of discrete random variables that would be of interest to the manager of a clothing store.
Give the z-score for a measurement from a normal distribution for the following:a. 1 standard deviation above the meanb. 1 standard deviation below the meanc. Equal to the meand. 2.5 standard
Suppose the random variable x is best described by a normal distribution with μ = 30 and σ = 4. Find the z-score that corresponds to each of the following x values: a. x = 20 b. x = 30 c. x =
Suppose x is a normally distributed random variable with μ = 11 and σ = 2. Find each of the following:a. P(10 ≤ x ≤ 12)b. P(6 ≤ x ≤ 10)c. P(13 ≤ x ≤ 16)d. P(7.8 ≤ x ≤ 12.6)e. P(x
Suppose x is a normally distributed random variable with μ = 50 and σ = 3. Find a value of the random variable, call it x0, such thata. P(x ≤ x0) = .8413b. P(x > x0) = .025c. P(x > x0) =
Suppose x is a binomial random variable with p = .4 and n = 25.a. Would it be appropriate to approximate the probability distribution of x with a normal distribution? Explain.b. Assuming that a
Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each of 992 senior managers at CPA firms. The
The study measured choice scores (on a scale of 0 to 100, where higher scores indicate a greater preference for vice options) for consumers shopping under each of the two conditions. Recall that the
The probability distribution shown here describes a population of measurements that can assume values of 0, 2, 4, and 6, each of which occurs with the same relative frequency:a. List all the
Consider the following probability distribution:a. Find µ.b. For a random sample of n = 3 observations from this distribution, find the sampling distribution of the sample mean.c. Find the sampling
Use the computer to generate 500 samples, each containing n = 25 measurements, from a population that contains values of x equal to 1, 2, 48, 49, 50. Assume that these values of x are equally likely.
a. Show that is an unbiased estimator of LL. b. Finder σ2?. c. Find the probability that will fall within 2σ of µ. For Information: Refer to Exercise 5.3.
a. Find the sampling distribution of s2.b. Find the population variance σ2.c. Show that s2 is an unbiased estimator of σ2.d. Find the sampling distribution of the sample standard deviation s.e.
The sampling distribution of the sample median. Is the median an unbiased estimator of the population mean µ? For Information: Refer to Exercise 5.5.
Suppose a random sample of n = 25 measurements is selected from a population with mean p and standard deviation σ. For each of the following values of µ and σ, give the values of µ and σ. a.
Suppose a random sample of n measurements is selected from a population with mean µ = 100 and variance σ2 = 100. For each of the following values of n, give the mean and standard deviation of the
A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and a standard deviation equal to 16. a. Give the mean and standard deviation of the (repeated) sampling
Refer to Exercise 5.18. Find the probability thata. x̅ is less than 16.b. x̅ is greater than 23.c. x̅ is greater than 25.d. x̅ falls between 16 and 22.e. x̅ is less than 14.
Simulate sampling from the population described in Exercise 5.1 by marking the values of x, one on each of four identical coins (or poker chips, etc.). Place the coins (marked 0, 2, 4, and 6) into a
A random sample of n = 900 observations is selected from a population with µ = 100 and σ = 10. a. What are the largest and smallest values of that you would expect to see? b. How far, at the
Consider a population that contains values of x equal to 0, 1, 2, ...,97, 98, 99. Assume that the values of x are equally likely. For each of the following values of n, use a computer to generate 500
In Exercise 2.33 you learned that phishing describes an attempt to extract personal/financial information from unsuspecting people through fraudulent e-mail. Data from an actual phishing attack
According Mi to a National Business Travel Association (NBTA) 2010 survey, the average salary of a travel management professional is $96,850. Assume that the standard deviation of such salaries is
Corporate sustainability, recall, refers to business practices designed around social and environmental considerations The level of support senior managers have for corporate sustainability was
Recall that researchers found that the time x (in hours) until the first critical-part failure is exponentially distributed with µ = .10 and σ = .10. Now consider a random sample of n = 50 NASCAR
Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste. Refer to the Plant Science (May 2010) investigation of the ability of a hybrid
In Exercise 4.139 you learned that Brighton Webs LTD modeled the arrival time of requests to a Web server within each hour using a uniform distribution. Specifically, the number of seconds x from the
Geotechnical engineers use water-level "manometer" surveys to assess the levelness of newly constructed concrete slabs. Elevations are typically measured at eight points on the slab; of interest is
Consider the population described by the probability distribution shown below.The random variable x is observed twice. If these observations are independent, verify that the different samples of size
Recall that a scanning probe instrument was used to measure the surface roughness x (in micrometers) of 20 sampled sections of coated interior pipe. Consider the sample mean, x.a. Assume that the
Perfluorooctanoic acid (PFOA) is a chemical used in Teflon-coated cookware to prevent food from sticking. The EPA is investigating the potential risk of PFOA as a cancer-causing agent (Science News
National Car Rental Systems, Inc., commissioned the U.S. Automobile Club (USAC) to conduct a survey of the general condition of the cars rented to the public by Hertz, Avis, National, and Budget
Convicted drug dealers were scored on the Wanting Recognition (WR) Scale -a scale that provides a quantitative measure of a person's level of need for approval and sensitivity to social situations.
Plastic fill process. University of Louisville researchers J. Usher, S. Alexander, and D. Duggins examined the process of filling plastic pouches of dry blended biscuit mix (Quality Engineering, Vol.
The British Medical Jou (Aug. 17, 2002) published the results of a study to comp the effectiveness of hand washing with soap and handrubh with alcohol. Health care workers who used handrubb had a
Suppose a random sample of n measurements is selected from a binomial population with probability of success p = .2. For each of the following values of n, give the mean and standard deviation of the
Suppose a random sample of n = 500 measurements is selected from a binomial population with probability of success p. For each of the following values of p, give the mean and standard deviation of
A random sample of n = 80 measurements is drawn from a binomial population with probability of success .3. a. Give the mean and standard deviation of the sampling distribution of the sample
A random sample of n = 250 measurements is drawn from a binomial population with probability of success .85. a. Find E(p̂) and σp̂. b. Describe the shape of the sampling distribution of p̂. c.
Find E(x) = µ. Then use the sampling distribution of found in Exercise 5.3 to find the expected value of . E() = µ. For Information: Refer to Exercise 5.3.
A random sample of n = 1,500 measurements is drawn from a binomial population with probability of success. What are the smallest and largest values of p̂ you would expect to see?
Consider a population with values of x equal to 0 or L Assume that the values of x are equally likely. For each of the following values of n, use a computer to generate 500 random samples and
The researchers obtained a random sample of 106 social robots through a Web search and determined the number that was designed with legs, but no wheels. Let p̂ represent the sample proportion of
According to a recent Pew Internet & American Life Project Survey (October 2010), 67% of adults who use the Internet have paid to download music. In a random sample of n = 1,000 adults who use
According to an AdweekJ Harris (July 2011) poll of U.S. adults, about 45% work during their summer vacation. Assume that the true proportion of all U.S. adults that work during summer vacation is p =
A study of full-time emergency medical service (EMS) workers published in the Journal of Allied Health (Fall 2011) found that only about 3% leave their job in order to retire. Assume that the true
The researchers found that the probability of a Finnish citizen investing in the stock market differed depending on IQ score. For those with a high IQ score, the probability is .44; for those with an
The study found that 40% of adult cell phone owners have downloaded an application ("app") to their cell phone. Assume this percentage applies to the population of all adult cell phone owners. a. In
Refer to the results of the 2009 North American Hotel Guest Satisfaction Index Study referenced in Exercise 4.48. Recall that 66% of hotel guests were aware of the hotel's "green" conservation
Recall that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. Consider a forensic database of 1,000 different pairs of
Assume that a random sample of n = 2 measurements is randomly selected from the population. a. List the different values that the sample median m may assume and find the probability of each. Then
Computer to generate 1,000 samples, each containing n = 11 observations, from a uniform distribution over the interval from 150 to 200. For this exercise, use a computer to generate 500 samples, each
Consider a population that contains values of x equal to 00,01,02,03,..., 96, 97, 98,99. Assume that these values of x occur with equal probability. Use a computer to generate 500 samples, each
Consider the following probability distribution:a. Find µ and Ïƒ2. b. Find the sampling distribution of the sample mean for a random sample of n = 2 measurements from this
Consider the following probability distribution: align="center">a. Calculate µ for this distribution.b. Find the sampling distribution of the sample mean for a random sample of n = 3
Refer to the Analytical Chemistry (Dec. 15, 2009) study of a new method used by GlaxoSmithKline Medicines Research Center to determine the amount of drug in a tablet. Drug concentrations (measured as
Recall that phishing describes an attempt to extract personal/financial information from unsuspecting people through fraudulent e-mail. The interarrival times (in seconds) for 267 fraud box e-mail
Refer to the Bulletin of Marine 0 Science (April 2010) observational study of teams fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise 6.29. Trap spacing measurements (in
Let t0 represent a particular value of t. Find the table values such that the following statements are true. a. P(t < t0) = .05 where df = 20 b. P(t > t0) = .005 where df = 9 c. P(t < - t0 or t < t0)
A random sample of 225 measurements is selected from a population, and the sample mean and standard deviation are = 32.5 and .s = 30.0, respectively. a. Use a 99% confidence interval to estimate

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