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statistics for experimentert

Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions

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 gestation periods. (Note: Users of the TI-83/84 Plus should simulate 500 human gestation periods.)c.
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 studied larval duration of the convict surgeonfish, a common tropical reef fish. This fish has been
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 curve required in Exercises 6.59–6.66. Sketch a standard normal curve and shade the area of
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 the area of each region.b. Complete the following table.Percentage of Region Area total area −∞
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% of all possible values of the variable exceed.d. Find the two values that divide the area under the
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 body is covered above by a shell, or carapace. From a recent article by F. Costa and F. Perez–Miles
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 cholesterol level of U.S. females 20 years old or older is normally distributed with a mean of 206
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 minutes.a. Determine the percentage of finishers who have times between 50 and 70 minutes.b. Determine
Water Consumption. The paper “Water Poverty in Urban India: A Study of Major Cities” explores water consumption in domestic households. The data collected from a few houses has a normal distribution with mean 105 liters and standard deviation 69.8 liters.Let x denote liters of water consumed.a.
Arterial Cord pH. Based on a recent study, the pH level of the arterial cord (one vessel in the umbilical cord) is normally distributed with mean 7.36 and standard deviation of 0.14. Find the percentage of preterm infants who have the following arterial cord pH levels.a. pH levels between 7.00 and
Elephant Pregnancies. G. Wittemeyer et al. studied demographic data on African elephants living in Kenya in the article “Comparative Demography of an At-Risk African Elephant Population”(PLOS ONE, Vol. 8. No. 1). Based on this study, we will assume that the time between pregnancies of the
Gibbon Song Duration. A preliminary behavioral study of the Jingdong black gibbon, a primate endemic to the Wuliang Mountains in China, found that the mean song bout duration in the wet season is 12.59 minutes with a standard deviation of 5.31 minutes.[SOURCE: L. Sheeran et al., “Preliminary
Friendship Motivation. In the article “Assessing Friendship Motivation During Preadolescence and Early Adolescence” (Journal of Early Adolescence, Vol. 25, No. 3, pp. 367–385), J. Richard and B. Schneider described the properties of the Friendship Motivation Scale for Children (FMSC), a scale
Brain Weights. According to a study, brain weights of men in country A are normally distributed with mean 1.47 kg and standard deviation 0.15 kg. Apply the empirical rule to complete each sentence. Complete parts (a) through (d).a. Complete the sentence “Approximately 68% of the men have brain
Alcohol Consumption. The World Health Organization(WHO)reported in the Global Status Report on Alcohol and Health 2014 that the mean worldwide consumption of alcohol in 2010 was 6.2 liters. Assume that the amount of alcohol consumed all over the world is normally distributed with a standard
Heights of Female Students. Refer to Example 6.3 on pages 267–268. The heights of the 3264 female students attending a midwestern college are approximately normally distributed with mean 64.4 inches and standard deviation 2.4 inches. Thus we can use the normal distribution with μ = 64.4 and σ =
Women’s Shoes. Research reveals that foot length of women is normally distributed with mean 9.58 inches and standard deviation 0.51 inch. This distribution is useful to shoe manufacturers, shoe stores, and related merchants because it permits them to make informed decisions about shoe production,
College-Math Success. 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,
Tipping. 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
In a recent study, the distances of certain raptor nests to the nearest marshland were studied. The study found that these distances are normally distributed with mean 4.38 km and standard deviation 0.86 km. Let Y be the distance of a randomly selected nest to the nearest marshland. Complete parts
Emergency Room Traffic. Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a mean of 8.7 minutes with a standard deviation of 8.7 minutes. Based solely on the values of these two parameters, explain
Let 0
Explain how to obtain normal scores from Table III in Appendix A when a sample contains equal observations.
Exam Scores. A sample of the final exam scores in a large introductory statistics course is as follows.88 67 64 76 86 85 82 39 75 34 90 63 89 90 84 81 96 100 70 96
Cellular Bills. 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).25 95 75 15 55 55 15 45 45 35 45 55 20 65 60
Sachin Tendulkar. Sachin Tendulkar is a former Indian cricket player who played international cricket from 1989 to 2013.The following table shows the number of runs he scored in 20 years of his entire career in one day international matches.0 239 417 704 319 1089 444 1141 412 1425 1611 1011 1894
Beverage Expenditures. 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 the following data, in
Suppose a sample of the height in inches of players in the starting lineup of a particular basketball team was obtained and shown below. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.a. Construct a normal probability
Skydiving Fatalities. In 2013, United States Parachute Association (USPA) recorded 24 fatal skydiving accidents in the U.S.out of roughly 3.2 million jumps. The data in the following table is the number of fatalities that occurred from 1999 to 2013.32 35 33 25 21 27 21 18 30 16 21 25 19 24 14
Oxygen Distribution. 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 et al. explored the
Medieval Cremation Burials. 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 England. Here are
The data set to the right is the body mass index of 20 men.Use technology to obtain a histogram and normal probability plot of the data and use them to assess the (approximate) normality of the data. 26.0 23.8 25.3 23.4 27.7 26.9 32.0 20.7 28.5 19.9 23.1 23.1 26.4 24.1 33.4 25.6 26.7 21.7 24.5
Vegetarians and Omnivores. 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), S. Lu et al.
“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 that there were at least 1000 chips in every 18-ounce bag of cookies that they examined. As part of
Finger Length of Criminals. 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 table
Household Expenditure. In a certain city, household expenditure is generally distributed with a mean of $460 and a standard deviation of $54.a. Use the technology of your choice to simulate four random samples of 100 houses each.b. Obtain a normal probability plot of each sample in part (a).c. Are
Emergency Room Traffic. 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 show that the mean
True–False Exams. Refer to Example 6.20 on page 320.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
True–False Exams. Refer to Example 6.20 on page 320.a. Use Table 6.7 to find the probability that the student gets i. 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
True–False Exams. 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?
True–False Exams. If, in Example 6.20, the true–false exam had 30 questions instead of 10, which normal curve would you use to approximate probabilities for the number of correct guesses?Applying the Concepts and Skills In Exercises 6.165–6.172, apply Procedure 6.3 on page 321 to approximate
Stalked College Women. In the article “Violence against Women: How Safe Are Our Institutions of Higher Learning?”(Family & Intimate Partner Violence Quarterly, Vol. 05, No. 04, pp. 341–349), researcher D. Thomas asserts that the population of students attending colleges and universities, and
Population. According to the Australian Bureau of Statistics, during a particular year, the country’s population was 17,843,000, out of which 22.6% were born overseas. If a sample of 200 people is selected at random out of the total population, what is the probability that the number of overseas
High School Graduates. According to the document Current Population Survey, published by the U.S. Census Bureau, 30.4%of U.S. adults 25 years old or older have a high school degree as their highest educational level. If 100 such adults are selected at random, determine the probability that the
Women. The World Health Organization publishes an annual report titled Women and Health, which studies the health of women from different geographic regions and age groups. During one year, 48.0% of all women from South-East Asia and Western Pacific regions were aged 60+. The total population of
Airline Reservations. A particular airline published that the no-show rate for reservations is 21%. In other words, the probability is 0.21 that a person making a reservation will not turn up to board the flight. For the next flight, 180 people have reservations. What is the probability thata.
Lightning-Induced Fatalities. As reported in an issue of Weatherwise, according to the National Oceanic and Atmospheric Administration, people at ballparks and playgrounds are in more danger of being struck by lightning than are those on golf courses. Of lightning-induced fatalities, 3.9% occur on
Android Lollipop. The article “Android Lollipop Running on Only 1.6% Units, Almost after Three Months of Launch” appearing on the Website bharatpress.com, says that about 39.7% of Android devices run on Android 4.4 KitKat. If 250 Android smartphones are collected at random, find the probability
Children’s Sleep Problems. Families and pediatricians often have difficulty managing sleep problems of young children. In the article “An Individualized and Comprehensive Approach to Treating Sleep Problems in Young Children” (Journal of Applied Behavioral Analysis, Vol. 46, No. 1, pp.
Roulette. An American roulette wheel consists of 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on each of the 38 numbers. A gambler is playing roulette and bets $10 on red each time. If the ball lands on a red
AA Battery Lifetimes. A brand of AA battery has normally distributed lifetimes with a mean of 28.4 hours and a standard deviation of 2.6 hours. A supermarket purchases 500 of these batteries from the manufacturer. What is the probability that at least 75% of them will last longer than 26 hours?
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. One in 1500 males is affected world-wide, with no ethnic bias.a. In a sample of 10,000 males, how many would you
use and understand the formulas in this chapter.
define, state the basic properties of, and apply density curves.
explain what it means for a variable to be normally distributed or approximately normally distributed.
explain the meaning of the parameters for a normal curve.
identify the basic properties of and sketch a normal curve.
identify the standard normal distribution and the standard normal curve.
use Table II to determine areas under the standard normal curve.
use Table II to determine the z-score(s) corresponding to a specified area under the standard normal curve.
use and understand the zα notation.
determine a percentage or probability for a normally distributed variable.
state and apply the empirical rule for variables.
determine the observations corresponding to a specified percentage or probability for a normally distributed variable.
explain how to assess the normality of a variable with a normal probability plot.
construct a normal probability plot with the aid of Table III.
use a normal probability plot to detect outliers.
approximate binomial probabilities by normal-curve areas, when appropriate.
The percentage of all possible observations of a variable that lie between 25 and 50 equals the area under its density curve between and , expressed as a percentage.
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 − x 2/4. Hint: First find the area to the right of x and
on page 285.What percentage of all possible observations of the variablec. lie between 1/2 and 1?d. are at least 1.5?
Answer true or false to each statement. Explain your answers.a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.b. Two normal distributions that have the same standard deviation have the same spread,
Consider the normal curves that have the parameters μ = 1.5 and σ = 3; μ = 1.5 and σ = 6.2; μ = −2.7 and σ = 3; μ = 0 andσ = 1.a. Which curve has the largest spread?b. Which curves are centered at the same place?c. Which curves have the same spread?d. Which curve is centered farthest to
Determine and sketch the area under the standard normal curve that liesa. to the left of −1.37.b. to the right of 0.55.c. between 1.47 and 2.09.d. between −0.03 and 1.44.e. between −2.57 and −1.75.f. either to the left of 1.23 or to the right of 1.45.
For the standard normal curve, find the z-score(s)a. that has area 0.30 to its left.b. that has area 0.10 to its right.c. z0.025, z0.05, z0.01, and z0.005.d. that divide the area under the curve into a middle 0.99 area and two outside 0.005 areas.Applying the Concepts and Skills
Dispensing Coffee. A coffee machine is supposed to dispense 12 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 11.50
Birth Weights. The WONDER database, maintained by the Centers for Disease Control and Prevention, provides a single point of access to a wide variety of reports and numeric public health data.From that database, we obtained the following data for one year’s birth weights of male babies who
Lower Limb Surgery. 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
Analytical GRE Scores. The Graduate Record Examination(GRE) is a standardized test that students usually take before entering graduate school. According to the document GRE Listening, Learning, Leading, a publication of the Educational Testing Service, the scores on the analytical portion of the
Analytical GRE Scores. Refer to Problem 28, and fill in the following blanks.a. Approximately 68% of students who took the analytical portion of the GRE scored between and .b. Approximately 95% of students who took the analytical portion of the GRE scored between and .c. Approximately 99.7% of
Northwest Atlantic Cod. 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
Mortgage Industry Employees. In an issue of National Mortgage News, a special report was published on publicly traded mortgage industry companies. A sample of 25 mortgage industry companies had the following numbers of employees.260 20,800 1,801 2,073 3,596 3,223 2,128 1,796 17,540 15 29,272 6,929
Interpret each of the following probability statements, using the frequentist interpretation of probability.a. The probability is 0.659 that a topper of the college is a girl.b. The probability of a particular dart hitting the target at the centre is 0.105.
Which of the following numbers could not possibly be a probability? Justify your answer.a. 7/99b. −0.3345c. 55/56
Which of the following numbers could not possibly be a probability? Justify your answer.a. 5/6b. 3.5c. 0 Applying the Concepts and Skills
Oklahoma State Officials. Refer to Table 4.1 on page 179.a. List the possible samples without replacement of size 3 that can be obtained from the population of five officials. (Hint: There are 10 possible samples.)If a simple random sample without replacement of three officials is taken from the
Oklahoma State Officials. Refer to Table 4.1 on page 179.a. List the possible samples without replacement of size 4 that can be obtained from the population of five officials. (Hint: There are five possible samples.)If a simple random sample without replacement of four officials is taken from the
Playing Cards. An ordinary deck of playing cards has 52 cards. There are four suits—spades, hearts, diamonds, and clubs—with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it isa. a
Blood Group. A group of 200 people are asked to write their blood group: 50 have A type, 65 have B type, 70 have O type and 15 have AB type. What is the probability that a persona. has A type?b. has A or AB type?c. does not have O type?
Pomegranate Peel. Pomegranate is an important fruit of the tropical and subtropical regions of the world. The fruit consists of three parts: the seed, the juice and the peel. The seed and the juice are known to be very beneficial, but the peel also has good qualities. The article‘‘Comparing

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