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Understandable Statistics Concepts And Methods 13th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Longevity: 90th Birthday It is estimated that 3.5%of the general population will live past their 90th birthday (Statistical Abstract of the United States, 112th edition). In a graduating class of 753 high school seniors, what is the probability that(a) 15 or more will live beyond their 90th
19. Guarantee: Package Delivery Express Courier Service has found that the delivery time for packages is normally distributed, with mean 14 hours and standard deviation 2 hours.(a) For a package selected at random, what is the probability that it will be delivered in 18 hours or less?(b) Inverse
Insurance: Claims Increasing the amount of your insurance claim in order to cover the amount of the deductible is a relatively common form of insurance fraud referred to as padding the claim. About 40% of all U.S. adults will try to pad their insurance claims!(Source: Are You Normal?, by Bernice
Health: Lead Contamination More than a decade ago, high levels of lead in the blood put 88% of children at risk. A concerted effort was made to remove lead from the environment. Now, according to the Third National Health and Nutrition Examination Survey (NHANES III) conducted by the Centers for
18. Guarantee: Disc Players Future Electronics makes compact disc players. Its research department found that the life of the laser beam device is normally distributed, with mean 5000 hours and standard deviation 450 hours.(a) Find the probability that the laser beam device will wear out in 5000
Critical Thinking Consider a binomial experiment with 20 trials and probability 0.45 of success on a single trial.(a) Use the binomial distribution to find the probability of exactly 10 successes.(b) Use the normal distribution to approximate the probability of exactly 10 successes.(c) Compare the
Critical Thinking You need to compute the probability of 5 or fewer successes for a binomial experiment with 10 trials. The probability of success on a single trial is 0.43. Since this probability of success is not in the table, you decide to use the normal approximation to the binomial. Is this an
Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n 5 40 trials and probability of success p 5 0.85.(a) Is it appropriate to use a normal approximation to this binomial distribution? Why?(b) Compute m and s of the approximating normal
17. Recycling: Aluminum Cans One environmental group did a study of recycling habits in a California community. It found that 70% of the aluminum cans sold in the area were recycled.(a) If 400 cans are sold today, what is the probability that 300 or more will be recycled?(b) Of the 400 cans sold,
Basic Computation: Normal Approximation to a Binomial Distribution Suppose we have a binomial experiment with n 5 40 trials and a probability of success p 5 0.50.(a) Is it appropriate to use a normal approximation to this binomial distribution? Why?(b) Compute m and s of the approximating normal
16. Customer Complaints: Time The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 9.3 minutes and a standard deviation of 2.5 minutes. What is the probability that for
Statistical Literacy When we use a normal distribution to approximate a binomial distribution, why do we make a continuity correction?AppendixLO1
Statistical Literacy Binomial probability distributions depend on the number of trials n of a binomial experiment and the probability of success p on each trial. Under what conditions is it appropriate to use a normal approximation to the binomial?AppendixLO1
15. Medical: Blood Type Blood type AB is found in only 3% of the population(Textbook of Medical Physiology, by A. Guyton, M.D.). If 250 people are chosen at random, what is the probability that(a) 5 or more will have this blood type?(b) between 5 and 10 will have this blood type?
Describe the sampling distribution for proportions pˆ.AppendixLO1
Approximate a binomial probability using the appropriate normal distribution probability.AppendixLO1
14. Basic Computation: Inverse Normal Find z such that 99% of the area under the standard normal curve lies between z and z.
Convert a range of r values to a corresponding range of normal x values using the continuity correction.AppendixLO1
13. Basic Computation: Inverse Normal Find z such that 5% of the area under the standard normal curve lies to the right of z.
Compute m and s for the normal approximation.AppendixLO1
12. Basic Computation: Probability Given that x is a normal variable with mean m 5 110 and standard deviation s 5 12, find(a) P1x 1202 (b) P1x 802 (c) P1108 x 1172
State the assumptions needed to use the normal approximation to the binomial distribution.AppendixLO1
Totals Instead of Averages: Escape Dunes It’s true—sand dunes in Colorado rival sand dunes of the Great Sahara Desert! The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height.However, like all sand dunes, they
11. Basic Computation: Probability Given that x is a normal variable with mean m 5 47 and standard deviation s 5 6.2, find(a) P1x 602 (b) P1x 502 (c) P150 x 602
10. Critical Thinking If x has a normal distribution with mean m 5 15 and standard deviation s 5 3, describe the distribution of x values for sample size n, where n 5 4, n 5 16 and n 5 100. How do the x distributions compare for the various sample sizes?
Totals Instead of Averages: Airplane Takeoff Time The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 2.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are
Totals Instead of Averages Let x be a random variable that represents checkout time (time spent in the actual checkout process) in minutes in the express lane of a large grocery. Based on a consumer survey, the mean of the x distribution is about m 5 2.7 minutes, with standard deviation s 5 0.6
9. Critical Thinking Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means x.(a) As the sample size becomes increasingly large, what distribution does the x distribution approach?(b) As the sample
Finance: European Growth Fund A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 100 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Based on information from Morningstar
Finance: Templeton Funds Templeton World is a mutual fund that invests in both U.S. and foreign markets. Let x be a random variable that represents the monthly percentage return for the Templeton World fund. Based on information from the Morningstar Guide to Mutual Funds (available in most
8. Statistical Literacy Give the formula for the standard error of the sample proportion pˆ distribution, based on n binomial trials with probability of success p on each trial.
Focus Problem: Impulse Buying Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a Denver Post article, the mean of the x distribution is about $20 and the estimated standard deviation is about $7.(a) Consider a random sample
7. Statistical Literacy Give the formula for the standard error of the sample mean x distribution, based on samples of size n from a distribution with standard deviation s.
6. Statistical Literacy For a normal distribution, is it likely that a data value selected at random is more than 2 standard deviations above the mean?
Wildlife: Deer Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in Mesa Verde National Park. Then x has a distribution that is approximately normal, with mean m 5 63.0 kg and standard deviation s 5 7.1 kg (Source: The Mule Deer
5. Statistical Literacy What characteristic of a normal quantile plot indicates that the data follow a distribution that is approximately normal?
4. Statistical Literacy Can a normal distribution always be used to approximate a binomial distribution? Explain.
3. Statistical Literacy Is a process in control if the corresponding control chart for data having a normal distribution shows a value beyond 3 standard deviations of the mean?
Medical: White Blood Cells Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean m 5 7500 and estimated standard deviation s 51750 (see reference in Problem 15). A test result
2. Statistical Literacy According to the empirical rule, approximately what percentage of the area under a normal distribution lies within 1 standard deviation of the mean? within 2 standard deviations? within 3 standard deviations?
Medical: Blood Glucose Let x be a random variable that represents the level of glucose in the blood(milligrams per deciliter of blood) after a 12-hour fast.Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean m 5 85 and estimated standard deviation
Vital Statistics: Heights of Men The heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard deviation 3 inches (based on information from Statistical Abstract of the United States, 112th edition).(a) What is the probability that an 18-year-old man
1. Statistical Literacy Describe a normal probability distribution.
4. In Chapter 2, we looked at the shapes of distributions. Review the concepts of skewness and symmetry; then categorize the following distributions as to skewness or symmetry:(a) A binomial distribution with n 5 11 trials and p 5 0.50(b) A binomial distribution with n 5 11 trials and p 5 0.10(c) A
Coal: Automatic Loader Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 75 tons of coal into each car.The actual weights of coal loaded into each car are normally distributed, with mean m 5 75
Critical Thinking Suppose an x distribution has mean m 5 5. Consider two corresponding x distributions, the first based on samples of size n 5 49 and the second based on samples of size n 5 81.(a) What is the value of the mean of each of the two x distributions?(b) For which x distribution is P(x .
Critical Thinking Suppose x has a distribution with m 515 and s 514.(a) If a random sample of size n 5 49 is drawn, find m , s x x, and P(15 # x # 17).(b) If a random sample of size n 5 64 is drawn, find m , s x x, and P(15 # x # 17).(c) Why should you expect the probability of part (b)to be higher
Critical Thinking Consider an x distribution with standard deviation s 512.(a) If specifications for a research project require the standard error of the corresponding x distribution to be 2, how large does the sample size need to be?(b) If specifications for a research project require the standard
3. In Chapter 3, we learned about means and standard deviations. In Section 5.1, we learned that probability distributions also can have a mean and standard deviation. Discuss what is meant by the expected value and standard deviation of a binomial distribution. How does this relate back to the
Critical Thinking Consider two x distributions corresponding to the same x distribution. The first x distribution is based on samples of size n 5100 and the second is based on samples of size n 5 225.Which x distribution has the smaller standard error?Explain.AppendixLO1
Critical Thinking Suppose x has a distribution with m 5 72 and s 5 8.(a) If random samples of size n 516 are selected, can we say anything about the x distribution of sample means?(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size
2. Why do we need to learn the formula for the binomial probability distribution?Using the formula repeatedly can be very tedious. To cut down on tedious calculations, most people will use a binomial table such as the one found in Appendix II of this book.(a) However, there are many applications
Statistical Literacy(a) If we have a distribution of x values that is more or less mound-shaped and somewhat symmetric, what is the sample size needed to claim that the distribution of sample means x from random samples of that size is approximately normal?(b) If the original distribution of x
Random samples of size n 5 36 are drawn.(a) Describe the x distribution and compute the mean and standard deviation of the distribution.(b) Find the z value corresponding to x 519.(c) Find P(x , 19).(d) Interpretation Would it be unusual for a random sample of size 36 from the x distribution to
Basic Computation: Central Limit Theorem Suppose x has a distribution with a mean of 20 and a standard deviation of AppendixLO1
Random samples of size n 5 64 are drawn.(a) Describe the x distribution and compute the mean and standard deviation of the distribution.(b) Find the z value corresponding to x 5 9.(c) Find P(x . 9).(d) Interpretation Would it be unusual for a random sample of size 64 from the x distribution to have
Basic Computation: Central Limit Theorem Suppose x has a distribution with a mean of 8 and a standard deviation of AppendixLO1
Statistical Literacy Describe how the variability of the x distribution changes as the sample size increases.AppendixLO1
Statistical Literacy List two unbiased estimators and their corresponding parameters.AppendixLO1
Statistical Literacy What is the standard deviation of a sampling distribution called?AppendixLO1
Statistical Literacy What is the standard error of a sampling distribution?AppendixLO1
Construct the approximate sampling distribution for x based on large samples from a distribution with known m and s using the Central Limit Theorem.AppendixLO1
Construct the theoretical sampling distribution for x from a normal distribution with known m and s .AppendixLO1
Critical Thinking Give an example of a specific sampling distribution we studied in this section.Outline other possible examples of sampling distributions from areas such as business administration, economics, finance, psychology, political science, sociology, biology, medical science, sports,
Critical Thinking How can relative frequencies be used to help us estimate probabilities occurring in sampling distributions?AppendixLO1
Critical Thinking How do frequency tables, relative frequencies, and histograms showing relative frequencies help us understand sampling distributions?AppendixLO1
Statistical Literacy What is a sampling distribution?AppendixLO1
Statistical Literacy What is the meaning of the term statistical inference? What types of inferences will we make about population parameters?AppendixLO1
Statistical Literacy What is a sample statistic? Give three examples.AppendixLO1
Statistical Literacy What is a population parameter?Give three examples.AppendixLO1
Statistical Literacy What is a random sample from a population? Hint: See Section 1.2.AppendixLO1
Statistical Literacy What is a population? Give three examples.AppendixLO1
Hypothesize the theoretical sampling distribution corresponding to the sampling distribution for x and pˆ .AppendixLO1
Construct a relative frequency histogram for pˆ values.AppendixLO1
Construct a relative frequency histogram for x values.AppendixLO1
Conditional Probability: Cycle Time A cement truck delivers mixed cement to a large construction site. Let x represent the cycle time in minutes for the truck to leave the construction site, go back to the cement plant, fill up, and return to the construction site with another load of cement. From
Conditional Probability Suppose you want to eat lunch at a popular restaurant. The restaurant does not take reservations, so there is usually a waiting time before you can be seated. Let x represent the length of time waiting to be seated. From past experience, you know that the mean waiting time
Budget: Maintenance The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean m 5$615 and standard deviation s 5$42.(a) If $646 is budgeted for next week, what is the
Exhibition Shows: Inverse Normal Distribution Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the doors opened, and the standard deviation was estimated at about 52
Convention Center: Exhibition Show Attendance Attendance at large exhibition shows in Denver averages about 8000 people per day, with standard deviation of about 500. Assume that the daily attendance figures follow a normal distribution.(a) What is the probability that the daily attendance will be
Insurance: Satellites A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.7 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London
Estimating the Standard Deviation: Veterinary Science How much should a healthy kitten weigh?A healthy 10-week-old (domestic) kitten should weigh an average of m 5 24.5 ounces with a (95%of data) range from 14 to 35 ounces. (See reference in Problem 33.) Let x be a random variable that represents
Estimating the Standard Deviation: Veterinary Science The resting heart rate for an adult horse should average about m 5 46 beats per minute with a (95% of data) range from 22 to 70 beats per minute, based on information from the Merck Veterinary Manual (a classic reference used in most veterinary
Estimating the Standard Deviation: Refrigerator Replacement Consumer Reports indicated that the average life of a refrigerator before replacement is m 514 years with a (95% of data) range from 9 to 19 years. Let x 5age at which a refrigerator is replaced.Assume that x has a distribution that is
Guarantee: Watches Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 28 months before certain electronic components deteriorate, causing the watch to become unreliable.The standard deviation of watch lifetimes is 5
Guarantee: Batteries Quick Start Company makes 12-volt car batteries. After many years of product testing, the company knows that the average life of a Quick Start battery is normally distributed, with a mean of 45 months and a standard deviation of 8 months.(a) If Quick Start guarantees a full
Law Enforcement: Police Response Time Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene (based on information from The Denver Post). Over a long period of time,
Archaeology: Hopi Village Thickness measurements of ancient prehistoric Native American pot shards discovered in a Hopi village are approximately normally distributed, with a mean of 5.1 millimeters(mm) and a standard deviation of 0.9 mm (Source:Homol’ovi II: Archaeology of an Ancestral Hopi
Medical: Blood Protoplasm Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults, x is approximately normally
Medical: Blood Glucose A person’s blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with
Find the z value such that 95% of the standard normal curve lies between 2z and z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1
Find the z value such that 98% of the standard normal curve lies between 2z and z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1
Find z such that 95% of the standard normal curve lies to the right of z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1
1. Discuss what we mean by a binomial experiment. As you can see, a binomial process or binomial experiment involves a lot of assumptions! For example, all the trials are supposed to be independent and repeated under identical conditions. Is this always true? Can we always be completely certain
Find z such that 82% of the standard normal curve lies to the right of z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1
Find z such that 5% of the standard normal curve lies to the right of z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1
Find z such that 8% of the standard normal curve lies to the right of z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1
Find z such that 97.5% of the standard normal curve lies to the left of z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1
Find z such that 55% of the standard normal curve lies to the left of z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1
Find z such that 5.2% of the standard normal curve lies to the left of z.In Problems 15–24, find the z value described and sketch the area described.AppendixLO1

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