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Understanding Basic Statistics 7th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Business Ethics: Privacy According to the same poll quoted in Problem 24, 53% of adults are concerned that Social Security numbers are used for general identifi cation. For a group of eight adults selected at random, we used Minitab to generate the binomial probability distribution and the
Binomial Distribution Table: Symmetry Study the binomial distribution table (Table 2 of the Appendix). Notice that the probability of success on a single trial p ranges from 0.01 to 0.95. Some binomial distribution tables stop at 0.50 because of the symmetry in the table. Let’s look for that
Statistical Literacy What does the expected value of a binomial distribution with n trials tell you?
Statistical Literacy Consider two binomial distributions, with n trials each.The fi rst distribution has a higher probability of success on each trial than the second. How does the expected value of the fi rst distribution compare to that of the second?
Basic Computation: Expected Value and Standard Deviation Consider a binomial experiment with n 5 8 trials and p 5 0.20.(a) Find the expected value and the standard deviation of the distribution.(b) Interpretation Would it be unusual to obtain 5 or more successes? Explain.Confi rm your answer by
Basic Computation: Expected Value and Standard Deviation Consider a binomial experiment with n 5 20 trials and p 5 0.40.(a) Find the expected value and the standard deviation of the distribution.(b) Interpretation Would it be unusual to obtain fewer than 3 successes?Explain. Confi rm your answer by
Critical Thinking Consider a binomial distribution of 200 trials with expected value 80 and standard deviation of about 6.9. Use the criterion that it is unusual to have data values more than 2.5 standard deviations above the mean or 2.5 standard deviations below the mean to answer the following
Critical Thinking Consider a binomial distribution with 10 trials. Look at Table 2 in the Appendix showing binomial probabilities for various values of p, the probability of success on a single trial.(a) For what value of p is the distribution symmetric? What is the expected value of this
Binomial Distribution: Histograms Consider a binomial distribution with n 5 5 trials. Use the probabilities given in Table 2 of the Appendix to make histograms showing the probabilities of r 5 0, 1, 2, 3, 4, and 5 successes for each of the following. Comment on the skewness of each distribution.(a)
Binomial Distributions: Histograms Figure 6-6 shows histograms of several binomial distributions with n 5 6 trials. Match the given probability of success with the best graph.(a) p 5 0.30 goes with graph _________.(b) p 5 0.50 goes with graph _________.(c) p 5 0.65 goes with graph _________.(d) p 5
Critical Thinking Consider a binomial distribution with n 5 10 trials and the probability of success on a single trial p 5 0.85.(a) Is the distribution skewed left, skewed right, or symmetrical?(b) Compute the expected number of successes in 10 trials.(c) Given the high probability of success p on
Critical Thinking Consider a binomial distribution with n 5 10 trials and the probability of success on a single trial p 5 0.05.(a) Is the distribution skewed left, skewed right, or symmetrical?(b) Compute the expected number of successes in 10 trials.(c) Given the low probability of success p on a
Marketing: Photography Does the kid factor make a difference? If you are talking photography, the answer may be yes! The following table is based on information from American Demographics (Vol. 19, No. 7).Ages of children in household, years Under 2 None under 21 Percent of U.S. households that buy
Quality Control: Syringes The quality-control inspector of a production plant will reject a batch of syringes if two or more defective syringes are found in a random sample of eight syringes taken from the batch. Suppose the batch contains 1% defective syringes.(a) Make a histogram showing the
Private Investigation: Locating People Old Friends Information Service is a California company that is in the business of fi nding addresses of long-lost friends. Old Friends claims to have a 70% success rate (Source: The Wall Street Journal). Suppose that you have the names of six friends for whom
Insurance: Auto The Mountain States Offi ce of State Farm Insurance Company reports that approximately 85% of all automobile damage liability claims are made by people under 25 years of age. A random sample of fi ve automobile insurance liability claims is under study.(a) Make a histogram showing
Education: Illiteracy USA Today reported that about 20% of all people in the United States are illiterate. Suppose you interview seven people at random off a city street.(a) Make a histogram showing the probability distribution of the number of illiterate people out of the seven people in the
Rude Drivers: Tailgating Do you tailgate the car in front of you? About 35% of all drivers will tailgate before passing, thinking they can make the car in front of them go faster (Source: Bernice Kanner, Are You Normal?, St. Martin’s Press). Suppose that you are driving a considerable distance on
Criminal Justice: Parole USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.(a) Find
Criminal Justice: Jury Duty Have you ever tried to get out of jury duty?About 25% of those called will fi nd an excuse (work, poor health, travel out of town, etc.) to avoid jury duty (Source: Bernice Kanner, Are You Normal?, St. Martin’s Press, New York). If 12 people are called for jury
Law Enforcement: Property Crime Does crime pay? The FBI Standard Survey of Crimes shows that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solved (Source: True Odds, by James Walsh, Merrit Publishing). Suppose a
Focus Problem: Personality Types We now have the tools to solve the Chapter Focus Problem. In the book A Guide to the Development and Use of the Myers–Briggs Type Indicators by Myers and McCaully, it was reported that approximately 45% of all university professors are extroverted. Suppose you
Criminal Justice: Convictions Innocent until proven guilty? In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials(Source: The Book of Risks, by Larry Laudan, John Wiley and Sons). Suppose you
Critical Thinking Let r be a binomial random variable representing the number of successes out of n trials.(a) Explain why the sample space for r consists of the set {0, 1, 2, . . . , n}and why the sum of the probabilities of all the entries in the entire sample space must be 1.(b) Explain why P1r
Expand Your Knowledge: Geometric Probability Distribution; Sociology GEOMETRIC DISTRIBUTION Suppose we have an experiment in which we repeat binomial trials until we get our fi rst success, and then we stop. Let n be the number of the trial on which we get our fi rst success. In this context, n is
Expand Your Knowledge: Geometric Distribution; Agriculture Approximately 3.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin (Source: Australian Journal of Agricultural Research, Vol. 25, pp. 783–790). (Bitter pit is a disease of
Expand Your Knowledge: Geometric Distribution; Fishing At Fontaine Lake Camp on Lake Athabasca in northern Canada, history shows that about 30%of the guests catch lake trout over 20 pounds on a 4-day fi shing trip (Source:Athabasca Fishing Lodges, Saskatoon, Canada). Let n be a random variable that
Probability Distribution: Auto Leases Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The results are as follows.Lease Length in Months Percent of Leases 13–24 12.7%25–36 37.1%37–48 28.5%49–60 21.5%More than 60 0.2%(a) Use the
Agriculture: Grapefruit It is estimated that 75% of a grapefruit crop is good;the other 25% have rotten centers that cannot be detected until the grapefruit are cut open. The grapefruit are sold in sacks of
Let r be the number of good grapefruit in a sack.(a) Make a histogram of the probability distribution of r.(b) What is the probability of getting no more than one bad grapefruit in a sack?What is the probability of getting at least one good grapefruit in a sack?(c) What is the expected number of
Statistical Literacy: Sample Space What is a statistical experiment? How could the magnetic susceptibility intervals 0 x 10, 10 x 20, and so on, be considered events in the sample space of all possible readings?
Statistical Literacy: Probability What is probability?What do we mean by relative frequency as a probability estimate for events? What is the law of large numbers? How would the law of large numbers apply in this context?
Statistical Literacy: Probability Distribution Do the probabilities shown in Table A add up to 1? Why should they total to 1?
Probability Rules For a site chosen at random, estimate the following probabilities.(a) P10 x 302 (b) P110 x 402(c) P1x 202 (d) P1x 202(e) P130 x2 (f) P(x not less than 10)(g) P10 x 10 or 40 x2(h) P140 x and 20 x2
Discrete Probability Distribution Consider the midpoint of each interval. Assign the value 45 as the midpoint for the interval 40 x. The midpoints constitute the sample space for a discrete random variable. Using Table A, compute the expected value m and the standard deviation s.Midpoint x 5 15
Binomial Distribution Suppose a reading between 30 and 40 is called “very interesting” from an archaeological point of view. Let us say you take readings at n 5 12 sites chosen at random. Let r be a binomial random variable that represents the number of “very interesting” readings from
Linear Regression: Blood Glucose Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast).Units are in mg/10 ml. A random sample of eight adults gave
Statistical Literacy Which, if any, of the curves in Figure 7-7 look(s) like a normal curve? If a curve is not a normal curve, tell why.
Statistical Literacy Look at the normal curve in Figure 7-8, and fi nd m, m 1 s, and s.
3. Critical Thinking Look at the two normal curves in Figures 7-9 and 7-10.Which has the larger standard deviation? What is the mean of the curve in Figure 7-9? What is the mean of the curve in Figure 7-10?
Critical Thinking Sketch a normal curve(a) with mean 15 and standard deviation 2.(b) with mean 15 and standard deviation 3.(c) with mean 12 and standard deviation 2.(d) with mean 12 and standard deviation 3.(e) Consider two normal curves. If the fi rst one has a larger mean than the second one,
Basic Computation: Empirical Rule What percentage of the area under the normal curve lies(a) to the left of m?(b) between m s and m 1 s?(c) between m 3s and m 1 3s?
Basic Computation: Empirical Rule What percentage of the area under the normal curve lies(a) to the right of m?(b) between m 2s and m 1 2s?(c) to the right of m 1 3s?
Distribution: Heights of Coeds Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches (based on information from Statistical Abstract of the United States, 112th Edition), answer the following questions. Hint: Use Problems 5 and 6
Distribution: Rhode Island Red Chicks The incubation time for Rhode Island Red chicks is normally distributed with a mean of 21 days and standard deviation of approximately 1 day (based on information from World Book Encyclopedia). Look at Figure 7-3 and answer the following questions. If 1000 eggs
Vending Machine: Soft Drinks A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6 ounces and standard deviation of 0.4 ounce.Examine Figure 7-3 and answer the following questions.(a) Estimate the
Expand Your Knowledge: Continuous Uniform Probability Distribution Let a and b be any two constants such that ab. Suppose we choose a point x at random in the interval from a tob. In this context the phrase at random is taken to mean that the point x is as likely to be chosen from one particular
Uniform Distribution: Measurement Errors Measurement errors from instruments are often modeled using the uniform distribution (see Problem 12). To determine the range of a large public address system, acoustical engineers use a method of triangulation to measure the shock waves sent out by the
Statistical Literacy What does a standard score measure?
Statistical Literacy Does a raw score less than the mean correspond to a positive or negative standard score? What about a raw score greater than the mean?
Statistical Literacy What is the value of the standard score for the mean of a distribution?
Statistical Literacy What are the values of the mean and standard deviation of a standard normal distribution?
Basic Computation: z Score and Raw Score A normal distribution has m 5 30 and s 5 5.(a) Find the z score corresponding to x 5 25.(b) Find the z score corresponding to x 5 42.(c) Find the raw score corresponding to z 5 2.(d) Find the raw score corresponding to z 5 1.3.
Basic Computation: z Score and Raw Score A normal distribution has m 5 10 and s 5 2.(a) Find the z score corresponding to x 5 12.(b) Find the z score corresponding to x 5 4.(c) Find the raw score corresponding to z 5 1.5.(d) Find the raw score corresponding to z 5 1.2.
Critical Thinking Consider the following scores:(i) Score of 40 from a distribution with mean 50 and standard deviation 10(ii) Score of 45 from a distribution with mean 50 and standard deviation 5 How do the two scores compare relative to their respective distributions?
Critical Thinking Raul received a score of 80 on a history test for which the class mean was 70 with standard deviation
He received a score of 75 on a biology test for which the class mean was 70 with standard deviation 2.5. On which test did he do better relative to the rest of the class?
z Scores: First Aid Course The college physical education department offered an advanced fi rst aid course last semester. The scores on the comprehensive fi nal exam were normally distributed, and the z scores for some of the students are shown below:Robert, 1.10 Juan, 1.70 Susan, 2.00 Joel, 0.00
z Scores: Fawns Fawns between 1 and 5 months old in Mesa Verde National Park have a body weight that is approximately normally distributed with mean m 5 27.2 kilograms and standard deviation s 5 4.3 kilograms (based on information from The Mule Deer of Mesa Verde National Park, by G. W. Mierau and
z Scores: Red Blood Cell Count Let x 5 red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean m 5 4.8 and standard deviation s 5 0.3 (based on information from Diagnostic Tests with Nursing Implications,
Normal Curve: Tree Rings Tree-ring dates were used extensively in archaeological studies at Burnt Mesa Pueblo (Bandelier Archaeological Excavation Project: Summer 1989 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University Department of Anthropology). At one site on the
To the right of z 5 0 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the left of z 5 0 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the left of z 5 1.32 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the left of z 5 0.47 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the left of z 5 0.45 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the left of z 5 0.72 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the right of z 5 1.52 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the right of z 5 0.15 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the right of z 5 1.22 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
To the right of z 5 2.17 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
Between z 5 0 and z 5 3.18 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
Between z 5 0 and z 5 1.93 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
Between z 5 2.18 and z 5 1.34 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
Between z 5 1.40 and z 5 2.03 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
Between z 5 0.32 and z 5 1.92 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
Between z 5 1.42 and z 5 2.17 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
Between z 5 2.42 and z 5 1.77 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
Between z 5 1.98 and z 5 0.03 Basic Computation: Finding Areas Under the Standard Normal Curve In Problems 13–30, sketch the areas under the standard normal curve over the indicated intervals and fi nd the specifi ed areas.
P z 0 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 0 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 0.13 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 2.15 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 1.20 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 3.20 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 1.35 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 2.17 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 1.20 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P z 1.50 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 1.20 z 2.64 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 2.20 z 1.40 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 2.18 z 0.42 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 1.78 z 1.23 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 0 z 1.62 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 0 z 0.54 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 0.82 z 0 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 2.37 z 0 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
P 0.45 z 2.73 Basic Computation: Finding Probabilities In Problems 31–50, let z be a random variable with a standard normal distribution. Find the indicated probability, and shade the corresponding area under the standard normal curve.
Statistical Literacy What symbol is used for the arithmetic mean when it is a sample statistic? What symbol is used when the arithmetic mean is a population parameter?
Statistical Literacy Look at the formula for the mean. List the two arithmetic procedures that are used to compute the mean.

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