Question: The area under a particular normal curve

> Sketch a standard normal curve and shade the area of interest. Find the area under the standard normal curve that lies a. either to the left of −2.12 or to the right of 1.67. b. either to the left of 0.63 or to the right of 1.54.

> Sketch a standard normal curve and shade the area of interest. Determine the area under the standard normal curve that lies between a. −0.88 and 2.24. b. −2.5 and −2. c. 1.48 and 2.72. d. −5.1 and 1.

> Sketch a standard normal curve and shade the area of interest. Determine the area under the standard normal curve that lies between a. −2.18 and 1.44. b. −2 and −1.5. c. 0.59 and 1.51. d. 1.1 and 4.2.

> Sketch a standard normal curve and shade the area of interest. Find the area under the standard normal curve that lies to the right of a. 2.02. b. −0.56. c. −4.

> Sketch a standard normal curve and shade the area of interest. Find the area under the standard normal curve that lies to the right of a. −1.07. b. 0.6. c. 0. d. 4.2.

> Sketch a standard normal curve and shade the area of interest. Determine the area under the standard normal curve that lies to the left of a. −0.87. b. 3.56. c. 5.12.

> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The area under the density curve that lies to the left of 10 is 0.654. What percentage of all possible observations o

> Sketch a standard normal curve and shade the area of interest. Determine the area under the standard normal curve that lies to the left of a. 2.24. b. −1.56. c. 0. d. −4.

> The area under the standard normal curve that lies to the left of a z-score is always strictly between ____ and ____.

> Identify an advantage that the median and interquartile range have over the mean and standard deviation, respectively.

> In a study by A. Elliot et al., titled “Women’s Use of Red Clothing as a Sexual Signal in Intersexual Interaction” (Journal of Experimental Social Psychology, Vol. 49, Issue 3, pp. 599–602), women were studied to determine the effect of apparel color cho

> Explain how Table II is used to determine the area under the standard normal curve that lies a. to the left of a specified z-score. b. to the right of a specified z-score. c. between two specified z-scores.

> Why is the standard normal curve sometimes referred to as the z-curve?

> Property 4 of Key Fact 6.5 states that most of the area under the standard normal curve lies between −3 and 3. Use Table II to determine precisely the percentage of the area under the standard normal curve that lies between −3 and 3.

> According to Table II, the area under the standard normal curve that lies to the left of 1.96 is 0.975. Without further consulting Table II, determine the area under the standard normal curve that lies to the left of −1.96. Explain your reasoning.

> According to Table II, the area under the standard normal curve that lies to the left of 0.43 is 0.6664. Without further consulting Table II, determine the area under the standard normal curve that lies to the right of 0.43. Explain your reasoning.

> According to Table II, the area under the standard normal curve that lies to the left of −2.08 is 0.0188. Without further consulting Table II, determine the area under the standard normal curve that lies to the right of 2.08. Explain your reasoning.

> Without consulting Table II, explain why the area under the standard normal curve that lies to the right of 0 is 0.5.

> With which normal distribution is the standard normal curve associated?

> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The percentage of all possible observations of the variable that lie to the right of 4 equals the area under its dens

> Identify by name three important groups of percentiles.

> 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 studied larval duration of the convict surgeonfish, a common tropical reef fish.

> In a study by P. M. West titled “The Lion’s Mane” (American Scientist, Vol. 93, No. 3, pp. 226–236), the effects of the mane of a male lion as a signal of quality to mates and rivals was explored. Four life-sized dummies of male lions provided a tool for

> Refer to the simulation of human gestation periods discussed. a. Sketch the normal curve for human gestation periods. b. Simulate 1000 human gestation periods. c. Approximately what values would you expect for the sample mean and sample standard deviati

> 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 that there were at least 1000 chips in every 18-ounce bag of cookies that they examined. As part of th

> 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 WeissStats site. The total fertility rate gives the average number of chil

> 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 students. Student scores are reported on a scale that ranges from a

> 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 numb

> 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 of cloudiness, on a scale of 0 to 10, at Breslau (Wroclaw), Poland, during the decad

> 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 frequency distribution for birth rates during one year for the 50 sta

> From the document National Vital Statistics Reports, a publication of the National Center for Health Statistics, we obtained the following frequency distribution for the ages of women who became mothers during one year. a. Obtain a relative-frequency his

> A data set consists of 2m2 − 1 zeros, one −m, and one m. a. Compute x¯ and s for this data set. b. How many standard deviations from the mean is the observation m? c. Assuming that m ≥ 4, what percentage of the observations lie within three standard devi

> 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 S. Siikavuopio et al., we found that weights of adult green sea urchins are normal

> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The percentage of all possible observations of the variable that lie between 7 and 12 equals the area under its densi

> In a classic study, described by F. Yates in The Design and Analysis of Factorial Experiments (Commonwealth Bureau of Soils, Technical Communication No. 35), the effect on oat yield was compared for three different varieties of oats and four different co

> 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 minutes. Let x denote finishing time for finishers in this race. a. Sketch the distri

> According to the National Health and Nutrition Examination Survey, published by the National Center for Health Statistics, the serum (noncellular portion of blood) total cholesterol level of U.S. females 20 years old or older is normally distributed with

> 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 body is covered above by a shell, or carapace. From a recent article by F.

> Refer to Example. a. The area under the normal curve with parameters μ = 64.4 and σ = 2.4 that lies to the left of 61 is 0.0783. Use this information to estimate the percentage of female students who are shorter than 61 inches. b. Use the relative-freque

> Refer to Example. 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. Use your answer from part (a) to estimate the area under the normal curve having parameters μ

> 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

> 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 t

> How many standard deviations to either side of the mean must we go to ensure that, for any data set, at least 95% of the observations lie within?

> 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. Subsequentl

> 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 = 1/3

> 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

> A driver’s ability to detect highway signs is an important consideration in highway safety. In his dissertation, Highway Construction Safety and the Aging Driver, S. Younes investigated the distance at which drivers can first detect highway caution signs

> For a variable with a density curve, what is the relationship between the percentage of all possible observations of the variable that lie within any specified range and the corresponding area under its density curve.

> 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 x 2. What percent

> The area under a particular normal curve to the left of 105 is 0.6227. A normally distributed variable has the same mean and standard deviation as the parameters for this normal curve. What percentage of all possible observations of the variable lie to t

> For a normally distributed variable, what is the relationship between the percentage of all possible observations that lie to the right of 7 and the area under the associated normal curve to the right of 7? What if the variable is only approximately norm

> For a normally distributed variable, what is the relationship between the percentage of all possible observations that lie between 2 and 3 and the area under the associated normal curve between 2 and 3? What if the variable is only approximately normally

> How many standard deviations to either side of the mean must we go to ensure that, for any data set, at least 99% of the observations lie within?

> Sketch the normal distribution with a. μ = −2 and σ = 2. b. μ = −2 and σ = 1/2. c. μ = 0 and σ = 2.

> Sketch the normal distribution with a. μ = 3 and σ = 3. b. μ = 1 and σ = 3. c. μ = 3 and σ = 1.

> What are the parameters for a normal curve?

> True or false: The mean of a normal distribution has no effect on its spread. Explain your answer.

> Supermarkets are interested in strategies to increase temporarily the unit sales of a product. In one study, researchers compared the effect of display type and price on unit sales for a particular product. The following display types and pricing schemes

> As you learned on page 450, recent research by R. Brame et al. indicates that almost a third of Americans have been arrested by age 23, and this figure excludes arrests for minor traffic violations. Now that you have studied inferences for proportions, w

> Consider two normal distributions, one with mean −4 and standard deviation 3, and the other with mean −4 and standard deviation 6. Answer true or false to each statement and explain your answers. a. The two normal distributions have the same spread. b. T

> State the two basic properties of every density curve.

> Consider two normal distributions, one with mean −4 and standard deviation 3, and the other with mean 6 and standard deviation 3. Answer true or false to each statement and explain your answers. a. The two normal distributions have the same spread. b. Th

> Which normal distribution has a wider spread: the one with mean 1 and standard deviation 2 or the one with mean 2 and standard deviation 1? Explain your answer.

> Identify two methods for obtaining a simple random sample.

> Two normally distributed variables have the same means and the same standard deviations. What can you say about their distributions? Explain your answer.

> Precisely what is meant by the statement that a population is normally distributed?

> A variable is approximately normally distributed. If you draw a histogram of the distribution of the variable, roughly what shape will it have?

> Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a special type of reverse-J-shaped distribution called an exponential distribution. The records also s

> Explain in your own words why a density curve has the two properties listed.

> For humans, gestation periods are normally distributed with a mean of 266 days and a standard deviation of 16 days. a. Use the technology of your choice to simulate four random samples of 50 human gestation periods each. b. Obtain a normal probability pl

> In the journal article “Cardiac Resynchronization Therapy with or without an Implantable Defibrillator in Advanced Chronic Heart Failure” (New England Journal of Medicine, Vol. 350, pp. 2140–2150), M. Bristow et al. reported the results of a study of met

> In 1902, W. R. Macdonell published the article “On Criminal Anthropometry and the Identification of Criminals” (Biometrika,Vol. 1, pp. 177–227). Among other things, the author presented data on the left middle finger length, in centimeters. The following

> 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 that there were at least 1000 chips in every 18-ounce bag of cookies that they examined. As part of th

> Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper “LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores” (Journal of Nutrition, Vol. 130, pp. 1591–1596),

> What does Chebyshev’s rule say about the percentage of observations that lie within one standard deviation to either side of the mean? Discuss your answer.

> According to R. L. Polk & Co., the average age of passenger cars in the United States was 9.1 years in 2000. A sample of 37 passenger cars taken this year provided the ages, in years, displayed in the following table. Construct a dotplot for the ages.

> A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit

> In the article “Material Culture as Memory: Combs and Cremations in Early Medieval Britain” (Early Medieval Europe, Vol. 12, Issue 2, pp. 89–128), H. Williams discussed the frequency of cremation burials found in 17 archaeological sites in eastern Englan

> In the article “Distribution of Oxygen in Surface Sediments from Central Sagami Bay, Japan: In Situ Measurements by Microelectrodes and Planar Optodes” (Deep Sea Research Part I: Oceanographic Research Papers, Vol. 52, Issue 10, pp. 1974–1987), R. Glud e

> The following table provides the daily charges, in dollars, for a sample of 15 hotels and motels operating in South Carolina. The data were found in the report South Carolina Statistical Abstract, sponsored by the South Carolina Budget and Control Board.

> In the special report “Mousetrap: The Most-Visited Shoe and Apparel E-tailers” (Footwear News, Vol. 58, No. 3, p. 18), we found the following data on the average time, in minutes, spent per user per month from January to June of one year for a sample of

> The Bureau of Labor Statistics publishes information on average annual expenditures by consumers in the Consumer Expenditure Survey. In 2010, the mean amount spent by consumers on nonalcoholic beverages was $333. A random sample of 12 consumers yielded t

> A curve has area 0.613 to the left of 65 and area 0.287 to the right of 65. Could this curve be a density curve for some variable? Explain your answer.

> Prozac (fluoxetine hydrochloride), a product of Eli Lilly and Company, is used for the treatment of depression, obsessive–compulsive disorder (OCD), and bulimia nervosa. An issue of the magazine Arthritis Today contained an advertisement reporting on the

> The following table displays finishing times, in seconds, for the winners of fourteen 1-mile thoroughbred horse races, as found in Thoroughbred Times. a. use Table III in Appendix A to construct a normal probability plot of the given data. b. use part (a

> CTIA–The Wireless Association collects data on cell phones and publishes the results in Semi-annual Wireless Survey. A sample of 15 monthly cell-phone bills gave the following data (to the nearest dollar). a. use Table III in Appendix A to construct a no

> In 1905, R. Pearl published the article “Biometrical Studies on Man. I. Variation and Correlation in Brain Weight” (Biometrika, Vol. 4, pp. 13–104) in which he studied the brain weights of Swedish males. The brain weights of a random sample of 225 Swedis

> A sample of the final exam scores in a large introductory statistics course is as follows. a. use Table III in Appendix A to construct a normal probability plot of the given data. b. use part (a) to identify any outliers. c. use part (a) to assess the no

> Assess the normality of the variable under consideration.

> Assess the normality of the variable under consideration.

> Assess the normality of the variable under consideration.

> Assess the normality of the variable under consideration.

> Assess the normality of the variable under consideration.

> Assess the normality of the variable under consideration.

> Explain how to obtain normal scores from Table III in Appendix A when a sample contains equal observations

> In a designed experiment, there are two factors. One factor has m levels and the other factor has n levels. Determine the number of treatments.

> A curve has area 0.425 to the left of 4 and area 0.585 to the right of 4. Could this curve be a density curve for some variable? Explain your answer.

> The PGA TOUR provides various statistics on performance of players in the Professional Golfers’ Association of America. For the week ending September 9, 2013, the year-to-date leader for longest average drive was Bubba Watson. For his 773 drives, he aver

> How is a normal probability plot used to detect outliers?

> Explain in detail what a normal probability plot is and how it is used to assess the normality of a variable.