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Introductory Statistics 10th Edition Neil A. Weiss - Solutions

Suppose that P(Z > 1.96) = 0.025. Find P(Z ≤ 1.96).
We have provided the probability distributions of the random variables considered in Exercises 5.7-5.10 of Section 5.1. For each exercise, do the following tasks.a. Find the mean of the random variable.b. Obtain the standard deviation of the random variable by using one of the formulas given in
The random variable X is the crew size of a randomly selected shuttle mission between April 12, 1981 and July 8, 2011. Its probability distribution is as follows.We have provided the probability distributions of the random variables considered in Exercises 5.11-5.15 of Section 5.1. For each
The random variable Y is the number of major hurricanes for a randomly selected year between 1851 and 2012. Its probability distribution is as follows.We have provided the probability distributions of the random variables considered in Exercises 5.11-5.15 of Section 5.1. For each exercise, do the
The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919-1921 World Series, when it was a best of nine). From the document World Series History on the Baseball Almanac website, as of November 2013, the lengths of the World Series are as given in the
The technology consultancy Data-Genetics published the online document PIN analysis. In addition to analyzing PIN numbers, passwords trends were examined. Seven million all-numeric passwords were collected and yielded the following estimate of the probability distribution of the number of digits
Refer to Exercise 5.43. Assume that the number of breakdowns on different days are independent of one another. Let X and Y denote the number of breakdowns on each of two consecutive days.a. Complete the preceding joint probability distribution table.P({X = 0} & {Y = 2}) = P(X = 0) Â· P(Y = 2)=
The factory manager in Exercise 5.43 estimates that each breakdown costs the company $500 in repairs and loss of production. If W is the number of breakdowns in a day, then $500W is the cost of breakdowns for that day.a. Refer to the probability distribution shown in Exercise 5.43 and determine the
Under what three conditions are repeated trials of an experiment called Bernoulli trials?
Discuss the pros and cons of binomial probability tables.
Suppose that a simple random sample is taken from a finite population in which each member is classified as either having or not having a specified attribute. Fill in the following blanks.a. If sampling is with replacement, the probability distribution of the number of members sampled that have the
Compute 3!, 7!, 8!, and 9!.
Evaluate the following binomial coefficients.(a)(b) (c) (d)
Evaluate the following binomial coefficients.(a)(b) (c) (d)
Determine the value of each binomial coefficient(a)(b) (c) (d)
Pinworm infestation, which is commonly found in children, can be treated with the drug pyrantel pamoate. According to the Merck Manual, the treatment is effective in 90% of cases. Suppose that three children with pinworm infestation are given pyrantel pamoate.a. Considering a success in a given
A variable x of a finite population has the following frequency distribution:Suppose a member is selected at random from the population and let X denote the value of the variable x for the member obtained.a. Determine the probability distribution of the random variable X.b. Use random-variable
Use Procedure 5.1 on page 242 to solve part (g) of Exercise 5.65.In Procedure 5.1Step 1 Identify a success.Step 2 Determine p, the success probability.Step 3 Determine n, the number of trials.Step 4 The binomial probability formula for the number of successes, X, is
Use Procedure 5.1 on page 242 to solve part (g) of Exercise 5.66.In Procedure 5.1Step 1 Identify a success.Step 2 Determine p, the success probability.Step 3 Determine n, the number of trials.Step 4 The binomial probability formula for the number of successes, X, is
A poll commissioned by Friends of the Earth and conducted by the Mellman Group found that 72% of American voters are in favor of a carbon tax. Suppose that six voters in the United States are randomly sampled and asked whether they favor a carbon tax. Determine the probability that the number
A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of game-play. According to the article "Pathological Video Game Use among Youths: A Two-Year Longitudinal Study" (Pediatrics, Vol. 127, No. 2, pp. 319-329) by D. Gentile et al., in 2011, about 9% of
A variable y of a finite population has the following frequency distribution:Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained.a. Determine the probability distribution of the random variable Y.b. Use random-variable
Identify two uses of Poisson distributions
List the three requirements for repeated trials of an experiment to constitute Bernoulli trials.
The game of craps is played by rolling two balanced dice. A first roll of a sum of 7 or 11 wins; and a first roll of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is thrown. It can be shown that the probability is 0.493 that a player wins a
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 the specified attribute.a. If the sampling is done with replacement, identify the probability
According to the Arizona State University Enrollment Summary, a frequency distribution for the number of undergraduate students attending Arizona State University (ASU) in the Fall 2012 semester, by class level, is as shown in the following table. Here, 1 = freshman, 2 = sophomore, 3 = junior, and
An accounting office has six incoming telephone lines. The probability distribution of the number of busy lines, Y, is as follows.Use random-variable notation to express each of the following events.The number of busy lines isa. Exactly four.b. At least four.c. Between two and four, inclusive.d. At
Refer to the probability distribution displayed in the table in Problem 18.In P 18a. Find the mean of the random variable Y.b. On average, how many lines are busy?c. Compute the standard deviation of Y.d. Construct a probability histogram for Y; locate the mean; and show one-, two-, and
Use the binomial probability formula to solve Problem 13(g). Compare your results.
According to JAVMA News, a publication of the American Veterinary Medical Association, roughly 60% of U.S. households own one or more pets. Four U.S. households are selected at random. Use Table XI in Appendix A to solve the following problems.a. Find the probability that, of the four households
Refer to Problem 22.a. Draw a probability histogram for the random variable X.b. The selection of the four households was done without replacement.Strictly speaking, then, why is the probability distribution that you obtained in Problem 22(b) only approximately correct? What is the exact
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, Vol. 5, pp. 604-624). The study examined the number of calls to a wrong number from coin-box telephones in a large
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 partial probability histogram for X.c. Identify the shape of the probability distribution of X. Is this shape typical
In the article "Interstellar Pelting" (Scientific American, Vol. 288, No. 5, pp. 28-30), G. Musser explained that information on extra solar planets can be discerned from foreign material and dust found in our solar system. Studies show that 1 in every 100 meteoroids entering Earth's atmosphere is
The respiratory disease emphysema, which is most commonly caused by smoking, causes damage to the air sacs in the lungs. According to the National Center for Health Statistics report Data from the National Health Interview Survey, 1.5% of the adult American population suffer from emphysema. Of 100
Refer to Problem 27. Use both the binomial probabilities and Poisson probabilities that you obtained in parts (c) and (d), respectively, to find the probability that, in a sample of 100 randomly selected Americans, the number who suffer from emphysema is a. Exactly three. b. Between two and five,
Determine the value of each binomial coefficient(a)(b) (c) (d) (e) (f)
a. Let X denote the age of a randomly selected undergraduate student at UWEC. Obtain the probability distribution of the random variable X. Display the probabilities to six decimal places.b. Obtain a probability histogram or similar graphic for the random variable X.c. Determine the mean and
a. Determine the probability that at least 4 of the 155 golfers would get a hole in one on the sixth hole. Discuss your result.b. What assumptions did you make in solving part (a)? Do those assumptions seem reasonable to you? Explain your answer.As we reported at the beginning of this chapter, on
Umbilical cord blood analysis immediately after delivery is one way to measure the health of an infant after birth. Researchers G. Natalucci et al. used it as a predictor of brain maturation of preterm infants in the article "Functional Brain Maturation Assessed During Early Life Correlates with
Researchers S. Lesik and M. Mitchell explore the difficulty of predicting success in college-level mathematics in the article "The Investigation of Multiple Paths to Success in College-Level Mathematics" (Journal of Applied Research in Higher Education, Vol. 5, Issue 1, pp. 48-57). One of the
In the article "Are Christian/Religious People Poor Tippers?" (Journal of Applied Social Psychology, Vol. 43, Issue 5, pp. 928-935), M. Lynn and B. Katz report that, for customers who receive bad service, the mean percentage tip is 8.56% of the bill with a standard deviation of 5.37%. Let x
Let 0 < α < 1. For a normally distributed variable, show that 100 (1 − α)% of all possible observations lie within zα/2 standard deviations to either side of the mean, that is, between μ − zα/2 · σ and μ + zα/2 · σ?
Express the quartiles, Q1, Q2, and Q3, of a normally distributed variable in terms of its mean, μ, and standard deviation, σ?
Express the kth percentile, Pk, of a normally distributed variable in terms of its mean, μ, and standard deviation, σ?
Under what circumstances is using a normal probability plot to assess the normality of a variable usually better than using a histogram, stem-and-leaf diagram, or dot-plot?
In each of Exercises 6.121-6.126, we have provided a normal probability plot of data from a sample of a population. In each case, assess the normality of the variable under consideration.a.b. c.
The rule of thumb for using the normal approximation to the binomial is that both np and n(1 − p) are 5 or greater. Why is this restriction necessary?
In Exercises 6.143-6.160, X denotes a binomial random variable with parameters n and p. For each exercise, indicate which area under the appropriate normal curve would be determined to approximate the specified binomial probability. a. P(X = 8) b. P(X = 6) c. P(X < 7)
Refer to Example 6.20 on page 298. a. Use Table 6.7 to find the probability that the student gets i. Either four or five answers correct. ii. Between three and seven answers correct, inclusive. b. Apply Procedure 6.3 to approximate the probabilities in part (a) by areas under a normal curve.
Refer to Example 6.20 on page 298.a. Use Table 6.7 to find the probability that the student getsi. At most five answers correct.ii. At least six answers correct.b. Apply Procedure 6.3 to approximate the probabilities in part (a) by areas under a normal curve. Compare your answers.TABLE 6.7
If, in Example 6.20, the true-false exam had 25 questions instead of 10, which normal curve would you use to approximate probabilities for the number of correct guesses?
A brand of flashlight battery has normally distributed lifetimes with a mean of 30 hours and a standard deviation of 5 hours. A supermarket purchases 500 of these batteries from the manufacturer. What is the probability that at least 80% of them will last longer than 25 hours?
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. One in 1500 males is affected world-wide, with no ethnic bias. a. In a sample of 10,000 males, how many would you expect to have
A variable has the density curve whose equation is y = 2x 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 any number x between 0 and 1 equals x2. What percentage of all possible observations of the
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 any number x between 0 and 1 equals x. What percentage of all possible observations of the
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 minutes, that John waits for the train is a variable with density curve y = 1/30 for 0 < x < 30, and y = 0 otherwise. a.
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 bacteria can multiply, is smeared with a uniform suspension of bacteria. Subsequently, spots indicating colonies of bacteria
The loss, in millions of dollars, due to a fire in a commercial building is a variable with density curve y = 1 − x/2 for 0 < x < 2, and y = 0 otherwise. Using the fact that the area of a triangle equals one-half its base times its height, we find that the area under this density curve to the
Desert Samaritan Hospital in Mesa, Arizona, keeps records of its emergency-room traffic. Beginning at 6:00 P.M. on any given day, the elapsed time, in hours, until the first patient arrives is a variable with density curve y = 6.9e−6.9x for x > 0, and y = 0 otherwise. Here e is Euler's number,
Without consulting Table II, explain why the area under the standard normal curve that lies to the right of 0 is 0.5?
State the empirical rule as specialized to variables?
State the empirical rule for variables?
A coffee machine is supposed to dispense 6 fluid ounces (fl oz) of coffee into a paper cup. In reality, the amounts dispensed vary from cup to cup. In fact, the amount dispensed, in fl oz, is a variable with density curve y = 2 for 5.75 < x < 6.25, and y = 0 otherwise. a. Graph the density curve of
The study "Intrathecal Sufentanil versus Fentanyl for Lower Limb Surgeries - A Randomized Controlled Trial" (Journal of Anaesthesiology Clinical Pharmacology, Vol. 27, Issue 1, pp. 67-73) by P. Motiani et al. compares two different agents, intrathecal sufentail and fentanyl, used in enhancing the
Researchers M. Kroll et al. studied the influence of paternity on rates of mortality and development in eggs and larvae of Northwest Atlantic cod in the article, "Paternal Effects on Early Life History Traits in Northwest Atlantic Cod, Gadus morhua" (Journal of Applied Ichthyology, Vol. 29, Issue
A variable has the density curve with equation y = 1 − 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 any number x between 0 and 2 equals x − x2 / 4. What percentage of all possible observations
The winner of the 2012-2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows.a. Find the population mean height of the five players.b. For samples of size 2, construct a table similar to Table 7.2 on page 310. Use the
Each year, Forbes magazine publishes a list of the richest people in the United States. As of September 16, 2013, the six richest Americans and their wealth (to the nearest billion dollars) are as shown in the following table. Consider these six people a population of
Why should you generally expect some error when estimating a parameter (e.g., a population mean) by a statistic (e.g., a sample mean)? What is this kind of error called?
Why is obtaining the mean and standard deviation of x̅ a first step in approximating the sampling distribution of the sample mean by a normal distribution?
Does the sample size have an effect on the standard deviation of all possible sample means? Explain your answer.
Explain why increasing the sample size tends to result in a smaller sampling error when a sample mean is used to estimate a population mean.
The winner of the 2012-2013 National Basketball Association (NBA) championship was the Miami Heat. One possible starting lineup for that team is as follows.a. Determine the population mean height, Î¼, of the five players. b. Consider samples of size 2 without replacement. Use your
Research by R. Pyhala et al. shows that young adults who were born prematurely with very low birth weights (below 1500 grams) have higher blood pressure than those born at term. The study can be found in the article, "Blood Pressure Responses to Physiological Stress in Young Adults with Very Low
According to the U.S. Census Bureau publication Manufactured Housing Statistics, the mean price of new mobile homes is $65,100. Assume a standard deviation of $7200. Let x̅ denote the mean price of a sample of new mobile homes. a. For samples of size 50, find the mean and standard deviation
Alcohol consumption on college and university campuses has gained attention because undergraduate students drink significantly more than young adults who are not students. Researchers I. Balodis et al. studied binge drinking in undergraduates in the article "Binge Drinking in
As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults in each state who have completed a bachelor's degree is provided on the Weiss Stats site. Use the technology of your choice to solve the following problems. a. Obtain the standard
An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is $1150,
In the document Anthropometric Reference Data for Children and Adults, C. Fryer et al. present data from the National Health and Nutrition Examination Survey on a variety of human body measurements. A half-century ago, the mean height of (U.S.) women in their 20s was 62.6 inches. Assume that the
The foraging behavior of the western pygmy-possum was investigated in the article "Strategies of a Small Nectarivorous Marsupial, the Western Pygmy-Possum, in Response to Seasonal Variation in Food Availability" (Journal of Mammalogy, Vol. 96, No. 6, pp. 1525-1535) by D. Morrant and S. Petit. The
Refer to Problem 12.a. Find the percentage of all samples of four pygmy-possums that have mean weights within 0.225 g of the population mean weight of 8.5 g.b. Obtain the probability that the mean weight of four randomly selected pygmy-possums will be within 0.225 g of the population mean weight of
In 2010, the Internal Revenue Service (IRS) sampled 308,946 tax returns to obtain estimates of various parameters. Data were published in Statistics of Income, Individual Income Tax Returns. According to that document, the mean income tax per return for the returns sampled was $11,266. a. Explain
Edmunds.com publishes information on new car prices in Car Shopping Trends Report. During a recent year, Americans spent an average of $30,803 for a new car. Assume a standard deviation of $10,200. a. Identify the population and variable under consideration. b. For samples of 50 new car sales
Refer to Exercise 8.8 and find a point estimate for the population standard deviation (i.e., the standard deviation of the variable).In Exercise 8.8
According to eMarketer, the average time spent per day with digital media in 2010 was 3 hours and 14 minutes. For last year, a random sample of 20 American adults spent the following number of hours per day with digital media.Find and interpret a 90% confidence interval for last year's mean time
As reported by B. Warner and J. Rutledge in the paper "Checking the Chips Ahoy! Guarantee" (Chance, Vol. 12, Issue 1, pp. 10-14), a random sample of forty-two 18-ounce bags of Chips Ahoy! cookies yielded a mean of 1261.6 chips per bag with a standard deviation of 117.6 chips per bag. a. Determine a
The webpage "Bottlenose Dolphin" produced by the National Geographic Society provides information about the bottlenose dolphin. A random sample of 50 adult bottlenose dolphins have a mean length of 12.04 ft with a standard deviation of 1.03 ft. Find and interpret a 90% confidence interval for the
The annual update of U.S. Overseas Loans and Grants, informally known as the "Greenbook," contains data on U.S. government monetary economic and military assistance loans. The following table shows military assistance loans, in thousands of dollars, to a sample of 10 countries, as reported by the
Batting Averages. An issue of Scientific American revealed that the batting averages of major-league baseball players are normally distributed with mean .270 and standard deviation .031. a. Simulate 2000 samples of five batting averages each.b. Determine the sample mean and sample standard
In a national poll of 1039 U.S. adults, conducted November 7-10, 2013, Gallup asked "Roughly how much money do you think you personally will spend on Christmas gifts this year?". The data provided on the WeissStats site are based on the results of the poll. a. Determine a 95% upper confidence bound
Explain why the margin of error determines the accuracy with which a sample mean estimates a population mean.
The margin of error is also called the maximum error of the estimate. Explain why.
An issue with legalization of medical marijuana is "diversion," the process in which medical marijuana prescribed for one person is given, traded, or sold to someone who is not registered for medical marijuana use. Researchers S. Sautel et al. study the issue of diversion in the article "Medical
Multi-sensor data loggers were attached to free-ranging American alligators in a study conducted by Y. Watanabe for the article "Behavior of American Alligators Monitored by Multi-Sensor Data Loggers" (Aquatic Biology, Vol. 18, pp. 1-8). The mean duration for a sample of 68 dives was 338.0 seconds.
Recall that a simple random sample of 36 new mobile homes yielded the prices, in thousands of dollars, shown in Table 8.1 on page 332.We found the mean of those prices to be $63.28 thousand. a. Use this information and Procedure 8.1 on page 339 to find a 95% confidence interval for the mean price
Refer to Exercise 8.7 and find a point estimate for the population standard deviation (i.e., the standard deviation of the variable).In Exercise 8.7
Light-emitting diodes (LEDs) and compact fluorescent lights (CFLs) are lightbulbs that are supposed to last up to fifty times longer than old fashioned incandescent lightbulbs and also use less energy. Consumer Reports sampled eighteen different 60-watt LED and CFL lightbulbs. The following table
The Professional Golfer's Association of America (PGA) organizes golf tournaments for professional golfers. The following table lists the longest drives, in yards, recorded during a PGA tournament for a random sample of 26 golfers. Use the technology of your choice to decide whether applying the

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