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mathematics
statistics

Elementary Statistics 8th Edition Neil A. Weiss - Solutions

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 states and the District of Columbia.a. Obtain a
In the paper €œCloudiness: 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 decade
A classic study by F. Thorndike on the number of calls to a wrong number appeared in the paper €œApplications of Poisson€™s Probability Summation€ (Bell Systems Technical Journal, Vol. 5, pp. 604€“624). The study examined the number of calls to a wrong
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 low of 200 to a high of 800. Summary results
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 CD. The total fertility rate gives the average number of children that would be born if all women in a given
Consider a normal distribution with mean 5 and standard deviation 2. a. Sketch the associated normal curve. b. Use the footnote on page 244 to write the equation of the associated normal curve. c. Use the technology of your choice to graph the equation obtained in part (b). d. Compare the
Refer to the simulation of human gestation periods discussed in Example on page. 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 deviation of the 1000 observations?
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 found to delay
Explain why being able to obtain areas under the standard normal curve is important.
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.
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 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.
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.
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.
Determine the area under the standard normal curve that lies to the left of a. 2.24. b. −1.56. c. 0. d. −4.
Determine the area under the standard normal curve that lies to the left of a. −0.87 b. 3.56 c. 5.12
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.
Find the area under the standard normal curve that lies to the right of a. 2.02. b. −0.56. c. −4.
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.
The area under the density curve that lies to the left of 10 is 0.654. What percentage of all possible observations of the variable are a. Less than 10? b. At least 10?
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.
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.
Find the area under the standard normal curve that lies a. Either to the left of −1 or to the right of 2. b. Either to the left of −2.51 or to the right of −1.
Use Table II to obtain each shaded area under the standard normal curve.
Use Table II to obtain each shaded area under the standard normal curve.
In each part, find the area under the standard normal curve that lies between the specified z-scores, sketch a standard normal curve, and shade the area of interest. a. −1 and 1 b. −2 and 2 c. −3 and 3
The total area under the following standard normal curve is divided into eight regions.a. Determine the area of each region. b. Complete the following table.In Exercises, use Table II to obtain the required z-scores. Illustrate your work with graphs.
Obtain the z-score for which the area under the standard normal curve to its left is 0.025.
Determine the z-score for which the area under the standard normal curve to its left is 0.01.
Find the z-score that has an area of 0.75 to its left under the standard normal curve.
The area under the density curve that lies to the right of 15 is 0.324. What percentage of all possible observations of the variable a. Exceed 15? b. Are at most 15?
Obtain the z-score that has area 0.80 to its left under the standard normal curve.
Obtain the z-score that has an area of 0.95 to its right.
Obtain the z-score that has area 0.70 to its right.
Determine z0.33.
Determine z0.015.
Find the following z-scores. a. z0.03 b. z0.005
Obtain the following z-scores. a. z0.20 b. z0.06
Determine the two z-scores that divide the area under the standard normal curve into a middle 0.90 area and two outside 0.05 areas.
Determine the two z-scores that divide the area under the standard normal curve into a middle 0.99 area and two outside 0.005 areas.
Complete the following table.
The area under the density curve that lies between 30 and 40 is 0.832. What percentage of all possible observations of the variable are either less than 30 or greater than 40?
In this section, we mentioned that the total area under any curve representing the distribution of a variable equals 1. Explain why.
Let 0
Briefly, for a normally distributed variable, how do you obtain the percentage of all possible observations that lie within a specified range?
Explain why the percentage of all possible observations of a normally distributed variable that lie within two standard deviations to either side of the mean equals the area under the standard normal curve between −2 and 2.
What does the empirical rule say?
A variable is normally distributed with mean 6 and standard deviation 2. Find the percentage of all possible values of the variable that a. Lie between 1 and 7. b. Exceed 5. c. Are less than 4.
A variable is normally distributed with mean 68 and standard deviation 10. Find the percentage of all possible values of the variable that a. Lie between 73 and 80. b. Are at least 75. c. Are at most 90.
A variable is normally distributed with mean 10 and standard deviation 3. Find the percentage of all possible values of the variable that a. Lie between 6 and 7 b. Are at least 10 c. Are at most 17.5
A variable is normally distributed with mean 0 and standard deviation 4. Find the percentage of all possible values of the variable that a. Lie between −8 and 8 b. Exceed −1.5 c. Are less than 2.75
A variable is normally distributed with mean 6 and standard deviation 2. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the 85th percentile. c. Find the value that 65% of all possible values of the variable exceed. d. Find the two values that divide the area under
The area under the density curve that lies between 15 and 20 is 0.414. What percentage of all possible observations of the variable are either less than 15 or greater than 20?
A variable is normally distributed with mean 68 and standard deviation 10. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the 99th percentile. c. Find the value that 85% of all possible values of the variable exceed. d. Find the two values that divide the area
A variable is normally distributed with mean 10 and standard deviation 3. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the seventh decile. c. Find the value that 35% of all possible values of the variable exceed. d. Find the two values that divide the area
A variable is normally distributed with mean 0 and standard deviation 4. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the second decile. c. Find the value that 15% of all possible values of the variable exceed. d. Find the two values that divide the area
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 titled
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 mg/dL (milligrams per
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 with times between 50 and 70 minutes. b. Determine the percentage of
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 normally distributed with mean 52.0 g and
Drive for Show, Putt for Dough. An article by S. M. Berry titled “Drive for Show and Putt for Dough” (Chance, Vol. 12(4), pp. 50–54) discussed driving distances of PGA players. The mean distance for tee shots on the 1999 men’s PGA tour is 272.2 yards with a standard deviation of 8.12 yards.
A study of sizes of metastatic carcinoid tumors in the heart was conducted by U. Pandya et al. and reported in the article “Metastatic Carcinoid Tumor to the Heart: Echocardiographic-Pathologic Study of 11 Patients” (Journal of the American College of Cardiology, Vol. 40, pp. 1328–1332).
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. Assuming that song bout is normally distributed, determine the
What is a density curve, and why are such curves important? In each of Problems 2–4, assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct.
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 and σ = 1. a. Which curve has the largest spread? b. Which curves are centered at the same place? c. Which curves have the same shape? d. Which curve is centered
Explain how to use Table II 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
Explain how to use Table II to determine the z-score that has a specified area to its a. Left under the standard normal curve. b. Right under the standard normal curve.
State the 68.26 - 95.44 - 99.74 rule.
Roughly speaking, what are the normal scores corresponding to a sample of observations?
Forearm Length. In 1903, K. Pearson and A. Lee published a paper entitled “On the Laws of Inheritance in Man. I. Inheritance of Physical Characters” (Biometrika, Vol. 2, pp. 357–462). From information presented in that paper, forearm length of men, measured from the elbow to the middle
According to Table II, the area under the standard normal curve that lies to the left of 1.05 is 0.8531. Without further reference to Table II, determine the area under the standard normal curve that lies a. To the right of 1.05 b. To the left of −1.05 c. Between −1.05 and 1.05
Determine and sketch the area under the standard normal curve that lies a. To the left of −3.02 b. To the right of 0.61 c. Between 1.11 and 2.75 d. Between −2.06 and 5.02 e. Between −4.11 and −1.5. f. Either to the left of 1 or to the right of 3
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
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 weighed
Proteins in the knee provide measures of lubrication and wear. In the article “Composition of Joint Fluid in Patients Undergoing Total Knee Replacement and Revision Arthroplasty” (Biomaterials, Vol. 25, No. 18, pp. 4433–4445), D. Mazzucco, et al. hypothesized that the protein make-up in the
The Graduate Record Examination (GRE) is a standardized test that students usually take before entering graduate school. According to the document Interpreting Your GRE Scores, a publication of the Educational Testing Service, the scores on the verbal portion of the GRE are (approximately) normally
Refer to Problem, and fill in the following blanks. Approximately a. 68.26% of students who took the verbal portion of the GRE scored between and______. b. 95.44% of students who took the verbal portion of the GRE scored between and______. c. 99.74% of students who took the verbal portion of the
According to the AAA Daily Fuel Gauge Report, the national average price for regular unleaded gasoline on January 29, 2009, was $1.843. That same day, a random sample of 12 gas stations across the country yielded the following prices for regular unleaded gasoline.a. Use Table III to construct a
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.a. Obtain a normal probability plot of the data. b. Use part (a) to identify any outliers. c. Use
The area under a density curve that lies to the left of 60 is 0.364. What percentage of all possible observations of the variable are a. Less than 60? b. At least 60?
Recall from Chapter 1 (refer to page 30) that the Focus database and Focus sample contain information on the undergraduate students at the University of Wisconsin – Eau Claire (UWEC). Now would be a good time for you to review the discussion about these data sets. Begin by opening the Focus
On page 243, we presented a frequency distribution for data on chest circumference, in inches, for 5732 Scottish militiamen. As mentioned there, Adolphe Quetelet used a procedure for fitting a normal curve to the data based on the binomial distribution. Here you are to accomplish that task by using
The area under a density curve that lies between 5 and 6 is 0.728. What percentage of all possible observations of the variable are either less than 5 or greater than 6?
State two of the main reasons for studying the normal distribution.
Define a. Normally distributed variable b. Normally distributed population c. Parameters for a normal curve
Answer true or false to each statement. Give reasons for your answers. a. Two variables that have the same mean and standard deviation have the same distribution. b. Two normally distributed variables that have the same mean and standard deviation have the same distribution.
Population data: 2, 3, 5, 5, 7, 8.a. Find the mean, μ, of the variable.b. For each of the possible sample sizes, construct a table similar to Table 7.2 on page 281 and draw a dotplot for the sampling distribution of the sample mean similar to Fig. 7.1 on page 281.c. Construct a graph similar to
The winner of the 2008-2009 National Basketball Association (NBA) championship was the Los Angeles Lakers. One starting lineup for that team is shown in the following table.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
Repeat parts (b)-(e) of Exercise 7.11 for samples of size 1.b. For samples of size 2, construct a table similar to Table 7.2 on page 281. Use the letter in parentheses after each player's name to represent each player.c. Draw a dotplot for the sampling distribution of the sample mean for samples of
Repeat parts (b)-(e) of Exercise 7.11 for samples of size 3.b. For samples of size 2, construct a table similar to Table 7.2 on page 281. Use the letter in parentheses after each player's name to represent each player.c. Draw a dotplot for the sampling distribution of the sample mean for samples of
Repeat parts (b)-(e) of Exercise 7.11 for samples of size 4.b. For samples of size 2, construct a table similar to Table 7.2 on page 281. Use the letter in parentheses after each player's name to represent each player.c. Draw a dotplot for the sampling distribution of the sample mean for samples of
Repeat parts (b)-(e) of Exercise 7.11 for samples of size 5.b. For samples of size 2, construct a table similar to Table 7.2 on page 281. Use the letter in parentheses after each player's name to represent each player.c. Draw a dotplot for the sampling distribution of the sample mean for samples of
This exercise requires that you have done Exercises 7.11-7.15.a. Draw a graph similar to that shown in Fig. 7.3 for sample sizes of 1, 2, 3, 4, and 5.b. What does your graph in part (a) illustrate about the impact of increasing sample size on sampling error?c. Construct a table similar to Table 7.4
Each year, Forbes magazine publishes a list of the world's richest people. In 2009, the six richest people, their citizenship, and their wealth (to the nearest billion dollars) are as shown in the following table. Consider these six people a population of interest.a. Calculate the mean wealth,
Repeat parts (b)€“(e) of Exercise 7.17 for samples of size 1.b. For samples of size 2, construct a table similar to Table 7.2. (There are 15 possible samples of size 2.)c. Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.d. For a random sample of size 2,
Repeat parts (b)€“(e) of Exercise 7.17 for samples of size 3. (There are 20 possible samples.)b. For samples of size 2, construct a table similar to Table 7.2. (There are 15 possible samples of size 2.)c. Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.d.
Repeat parts (b)€“(e) of Exercise 7.17 for samples of size 4. (There are 15 possible samples.)b. For samples of size 2, construct a table similar to Table 7.2. (There are 15 possible samples of size 2.)c. Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.d.
Repeat parts (b)€“(e) of Exercise 7.17 for samples of size 5. (There are six possible samples.)b. For samples of size 2, construct a table similar to Table 7.2. (There are 15 possible samples of size 2.)c. Draw a dotplot for the sampling distribution of the sample mean for samples of size 2.d.
Repeat parts (b)€“(e) of Exercise 7.17 for samples of size 6. What is the relationship between the only possible sample here and the population?b. For samples of size 2, construct a table similar to Table 7.2. (There are 15 possible samples of size 2.)c. Draw a dotplot for the sampling
Suppose that a sample is to be taken without replacement from a finite population of size N. If the sample size is the same as the population size, a. How many possible samples are there? b. What are the possible sample means? c. what is the relationship between the only possible sample and the

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