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Questions and Answers of
Statistics
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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).
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
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
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
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
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
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
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
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
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
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 −
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
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.
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
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.
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
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
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
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
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
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
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
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
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.
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
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
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
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
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,
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
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
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
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
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
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.
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
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
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.
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
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
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
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
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
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.
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
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
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
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
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
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
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