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statistics for experimentert

Questions and Answers of Statistics For Experimentert

Pinworm Infestation. Use Procedure 5.1 on page 264 to solve part (g) of Exercise 5.65.
Psychiatric Disorders. Use Procedure 5.1 on page 264 to solve part (g) of Exercise 5.66.
Tossing a Coin. If we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time. But what is the probability that such a coin will come up heads exactly half
Rolling a Die. If we repeatedly roll a balanced die, then, in the long run, it will come up “4” about one-sixth of the time. But what is the probability that such a die will come up “4”
Horse Racing. According to the Daily Racing Form, the probability is about 0.67 that the favorite in a horse race will finish in the money (first, second, or third place). In the next five races,
HIV Patients. The probability is 0.182 that a person with HIV positive at the age of 20 years will live till 63 years of age. Among 6 HIV positive patients of 20 years, what is the probability that
Traffic Fatalities and Intoxication. The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the probability is 0.40 that a traffic
Multiple-Choice Exams. A student takes a multiple-choice exam with 15 questions, each with five possible selections for the answer. A passing grade is 40% or better. Suppose that the student was
Recidivism. In the Scientific American article “Reducing Crime: Rehabilitation is Making a Comeback,” R. Doyle examined rehabilitation of felons. One aspect of the article discussed recidivism of
Sampling and the Binomial Distribution. Refer to the discussion on the binomial approximation to the hypergeometric distribution that begins on page 267.a. If sampling is with replacement, explain
Sampling and the Binomial Distribution. Following is a gender frequency distribution for students in Professor Weiss’s introductory statistics class.Gender Frequency Male 25 Female 15 Two students
The Hypergeometric Distribution. In this exercise, we discuss the hypergeometric distribution in more detail. When sampling is done without replacement from a finite population, the hypergeometric
The Geometric Distribution. In this exercise, we discuss the geometric distribution, the probability distribution for the number of trials until the first success in Bernoulli trials. The geometric
The Poisson Distribution. Another important discrete probability distribution is the Poisson distribution, named in honor of the French mathematician and physicist Simeon Poisson (1781–1840).This
What conditions should be satisfied in order to approximate binomial probabilities by Poisson probabilities?
Suppose that we plan to approximate a binomial distribution with parameters n and p by a Poisson distribution. What is the parameter for the Poisson distribution?
Amusement Ride Safety. Approximately 297 million guests visit the 400 American amusement parks annually and take 1.7 billion safe rides. The National Safety Council publishes a report titled
Motel Reservations. M. Driscoll and N. Weiss discussed the modeling and solution of problems concerning motel reservation networks in “An Application of Queuing Theory to Reservation Networks”
Cherry Pies. At one time, a well-known restaurant chains sold cherry pies. Professor D. Lund of the University of Wisconsin -Eau Claire enlisted the help of one of his classes to gather data on the
Motor-Vehicle Deaths. According to Injury Facts, a publication of the National Safety Council, in the United States, the lifetime probability of dying in a motor-vehicle crash is 1 in 112. Use the
Prisoners. From the U.S. Census Bureau and the article“U.S. Prison Population Falls for Third Year” by B. Montopoli of CBS News, we found that about 1 in every 200 Americans are in prison. Use
The Challenger Disaster. In a letter to the editor that appeared in the February 23, 1987, issue of U.S. News and World Report, a reader discussed the issue of space-shuttle safety.
Fragile X Syndrome. The second-leading genetic cause of mental retardation is Fragile X Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals.According to
Holes in One. Refer to the case study on page 245. According to the experts, the odds against a PGA golfer making a hole in one are 3708 to 1; that is, the probability is 1 3709 . Use the Poisson
A Yellow Lobster! As reported by the Associated Press, a veteran lobsterman recently hauled up a yellow lobster less than a quarter mile south of Prince Point in Harpswell Cove, Maine. Yellow
Roughly speaking, you can use the Poisson probability formula to approximate binomial probabilities when n is large and p is small (i.e., near 0). Explain how to use the Poisson probability formula
use and understand the formulas in this chapter.
determine the probability distribution of a discrete random variable.
construct a probability histogram.
describe events by using random-variable notation, when appropriate.
use the frequentist interpretation of probability to understand the meaning of the probability distribution of a random variable.
find and interpret the mean and standard deviation of a discrete random variable.
compute factorials and binomial coefficients.
define and apply the concept of Bernoulli trials.
assign probabilities to the outcomes in a sequence of Bernoulli trials.
obtain binomial probabilities.
compute the mean and standard deviation of a binomial random variable.
obtain Poisson probabilities.
compute the mean and standard deviation of a Poisson random variable.
use the Poisson distribution to approximate binomial probabilities, when appropriate.
What does the probability distribution of a discrete random variable tell you?
Determine the value of each binomial coefficient.a. 8 3b. 8 5c. 6 6d. 10 2e. 40 4f. 100 0
Following are two probability histograms of binomial distributions. For each, specify whether the success probability is less than,equal to, or greater than 0.5.P(X = x)x(a)01234567 0.00 0.05 0.10
Explain how the special formulas for the mean and standard deviation of a binomial or Poisson random variable are derived.
Suppose that a simple random sample of size n is taken from a finite population in which the proportion of members having a specified attribute is p. Let X be the number of members sampled that have
ASU Enrollment Summary. According to the Arizona State University Enrollment Summary, a frequency distribution for the number of undergraduate students attending Arizona State University (ASU) in the
Busy Phone Lines. An administrative office has eight incoming telephone lines. The probability distribution of the number of busy lines, Y , is as follows.y 0123 4 56 78 P(Y = y) 0.033 0.124 0.202
Busy Phone Lines. Refer to the probability distribution displayed in the table in Problem 18.a. Find the mean of the random variable Y.b. On average, how many lines are busy?c. Compute the standard
Craps. Use the binomial probability formula to solve Problem 13(g). Compare your results.
Penalty Kicks. In the game of soccer, a penalty kick is a direct free kick, taken from 12 yards out from the goal on the penalty mark. According to the article “Penalty Kicks in Soccer: An
Pets. According to Australian Companion Animal Council Inc,a publication of the This publication of Animal Health Alliance of Australia (AHAA) reveals that roughly 63% of Australians households own
Pets. Refer to Problem 22.a. Draw a probability histogram for the random variable X.b. The selection of the six households was done without replacement. Strictly speaking, then, why is the
Wrong Number. A classic study by F. Thorndike on the number of calls to a wrong number appeared in the paper “Applications of Poisson’s Probability Summation” (Bell Systems Technical Journal,
Wrong Number. Refer to Problem 24.a. Obtain a table of probabilities for the random variable X, stopping when the probabilities become zero to three decimal places.b. Use part (a) to construct a
Complementary and Alternative Medicine. According to data available in National Health Statistics Reports Number 12, December 10, 2008 the frequencies and age-adjusted percentages of children under
Complementary and Alternative Medicine. Refer to Problem 27. Use both the binomial probabilities and Poisson probabilities that you obtained in parts (c) and (d), respectively, to find the
What is a density curve?
The percentage of all possible observations of the variable that lie between 7 and 12 equals the area under its density curve between and , expressed as a percentage.
The percentage of all possible observations of the variable that lie to the right of 4 equals the area under its density curve to the right of , expressed as a percentage.
Given that 42.5% of all possible observations of the variable exceed 5, determine the area under the density curve that lies to thea. right of 5.b. left of 5.
Explain in your own words why a density curve has the two properties listed in Key Fact 6.1 on page 285.
Precisely what is meant by the statement that a population is normally distributed?
Which normal distribution has a wider spread: the one with mean 3 and standard deviation 4 or the one with mean 4 and standard deviation 3? Explain your answer.
True or false: The mean of a normal distribution has no effect on its spread. Explain your answer.
A variable has the density curve whose equation is y = x/2 for 0 < x < 2, and y = 0 otherwise.a. Graph the density curve of this variable.b. Show that the area under this density curve to the left of
A variable has the density curve whose equation is y = 1 for 0 < x < 1, and y = 0 otherwise.a. Graph the density curve of this variable.b. Show that the area under this density curve to the left of
Waiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in
Bacteria on a Petri Dish. A petri dish is a small, shallow dish of thin glass or plastic, used especially for cultures in bacteriology.A 2-inch-radius petri dish, containing nutrients upon which
Earthquake. The loss, in thousands of lives, due to an earthquake in a certain area is a variable with density curve y = (x 3)/4 for 0 < x < 2, and y = 0 otherwise. The area under this density curve
Catalyst. A catalyst is a substance that alters the rate of a chemical reaction without undergoing any permanent change itself.A chemist, while adding a particular catalyst to a reaction, observes
Female College Students. Refer to Example 6.3 on page 289.a. Use the relative-frequency distribution in Table 6.1 to obtain the percentage of female students who are between 60 and 65 inches tall.b.
Female College Students. Refer to Example 6.3 on page 289.a. The area under the normal curve with parameters μ = 64.4 andσ = 2.4 that lies to the left of 61 is 0.0783. Use this information to
Serum Cholesterol Levels. According to the National Health and Nutrition Examination Survey, published by the National Center for Health Statistics, the serum (noncellular portion of blood) total
Water Consumption. In a 2008 paper by Abdul Shaban titled“Water Poverty in Urban India: A Study of Major Cities”, the quantity of water consumed in Indian households has been studied. The data
Green Sea Urchins. From the paper “Effects of Chronic Nitrate Exposure on Gonad Growth in Green Sea Urchin Strongylocentrotus droebachiensis” (Aquaculture, Vol. 242, No. 1–4, pp. 357–363)by
Youth in India. Selected Socio-Economic Statistics, a report by the Ministry of Statistics and Programme Implementation of India, depicts the socio-economic development of India through statistical
Birth Rates. The National Center for Health Statistics publishes information about birth rates (per 1000 population) in the document National Vital Statistics Report. The following table provides a
Cloudiness in Breslau. In the paper “Cloudiness: Note on a Novel Case of Frequency” (Proceedings of the Royal Society of London, Vol. 62, pp. 287–290), K. Pearson examined data on daily degree
Wrong Number. A classic study by F. Thorndike on the number of calls to a wrong number appeared in the paper “Applications of Poisson’s Probability Summation” (Bell Systems Technical Journal,
SAT Scores. Each year, thousands of high school students bound for college take the Scholastic Assessment Test (SAT). This test measures the verbal and mathematical abilities of prospective college
Fertility Rates. From the U.S. Census Bureau, in the document International Data Base, we obtained data on the total fertility rates for women in various countries. Those data are presented on the
“Chips Ahoy! 1,000 Chips Challenge.” Students in an introductory statistics course at the U.S. Air Force Academy participated in Nabisco’s “Chips Ahoy! 1,000 Chips Challenge” by confirming
Gestation Periods of Humans. Refer to the simulation of human gestation periods discussed in Example 6.4 on page 292.a. Sketch the normal curve for human gestation periods.b. Simulate 1000 human
Delaying Adulthood. In the paper, “Delayed Metamorphosis of a Tropical Reef Fish (Acanthurus triostegus): A Field Experiment” (Marine Ecology Progress Series, Vol. 176, pp. 25–38), M. McCormick
The area under the standard normal curve that lies to the left of a z-score is always strictly between and .Applying the Concepts and Skills Use Table II to obtain the areas under the standard normal
Determine the area under the standard normal curve that lies to the left ofa. 0.92.b. −3.56.c. −1.29.
Findthe area underthe standard normal curvethatliestothe right ofa. −1.07.b. 0.6.c. 0.d. 4.2.
Determine the area under the standard normal curve that lies betweena. −0.92 and 3.56.b. −1.29 and −0.44.c. 0.48 and 0.92.d. −2.1 and 2.3.
Find the area under the standard normal curve that liesa. either to the left of −0.39 or to the right of 2.55.b. either to the left of −2.87 or to the right of −0.39.2 −1 1 2 3 za. Determine
Obtain the z-score that has area 0.33 to its right.
Determine z0.70.
Determine z0.015.
Find the following z-scores.a. z0.03b. z0.005
Complete the following table.z0.10 z0.05 z0.025 z0.01 z0.005 1.28 Extending the Concepts and Skills
Let 0
A variable is normally distributed with mean 15 and standard deviation 4. Find the percentage of all possible values of the variable thata. lie between 9 and 12.b. are at least 16.c. are at most 20.
A variable is normally distributed with mean 0 and standard deviation 3.a. Determine and interpret the quartiles of the variable.b. Obtain and interpret the second decile.c. Find the value that 23%
Giant Tarantulas. One of the larger species of tarantulas is the Grammostola mollicoma, whose common name is the Brazilian giant tawny red. A tarantula has two body parts. The anterior part of the
Serum Cholesterol Levels. According to the National Health and Nutrition Examination Survey, published by the National Center for Health Statistics, the serum (noncellular portion of blood) total
New York City 10-km Run. As reported in Runner’s World magazine, the times of the finishers in the New York City 10-km run are normally distributed with mean 61 minutes and standard deviation 9

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