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Understanding Basic Statistics 6th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $1 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the
The college student senate is sponsoring a spring break Caribbean cruise raffle. The proceeds are to be donated to the Samaritan Center for the Homeless. A local travel agency donated the cruise, valued at $2000. The students sold 2852 raffle tickets at $5 per ticket. (a) Kevin bought six tickets.
Jim is a 60-year-old Anglo male in reasonably good health. He wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided by the Vital Statistics section of
Sara is a 60-year-old Anglo female in reasonably good health. She wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until she is 65. The policy will expire on her 65th birthday. The probability of death in a given year is provided by the Vital Statistics
Which of the following are continuous variables, and which are discrete? (a) Speed of an airplane (b) Age of a college professor chosen at random (c) Number of books in the college bookstore (d) Weight of a football player chosen at random (e) Number of lightning strikes in Rocky Mountain National
Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer.(a)(b)
Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the possible values of x? Explain or give an example.
Consider the probability distribution shown in Problem 3(a). Compute the expected value and the standard deviation of the distribution.
For a fundraiser, 1000 raffle tickets are sold and the winner is chosen at random. There is only one prize, $500 in cash. You buy one ticket. (a) What is the probability you will win the prize of $500? (b) Your expected earnings can be found by multiplying the value of the prize by the probability
We can use the random-number table to simulate outcomes from a given discrete probability distribution. Jose plays basketball and has probability 0.7 of making a free-throw shot. Let x be the random variable that counts the number of successful shots out of 10 attempts. Consider the digits 0
What is the age distribution of promotion-sensitive shoppers? A supermarket super shopper is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon. The following table is based on information taken from Trends in the United States (Food Marketing
What is the income distribution of super shoppers (see Problem 8)? In the following table, income units are in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars.(a) Using the income midpoints x and
Central Eye Clinic advertises that 90% of its patients approved for LASIK surgery to correct vision problems have successful surgeries. (a) In the random-number table, assign the digits 0 through 8 to the event “successful surgery” and the digit 9 to the event “unsuccessful surgery.” Does
Consider a binomial experiment with n = 7 trials where the probability of success on a single trial is p = 0.30. (a) Find P(r = 0). (b) Find P(r ≥ 1) by using the complement rule.
Consider a binomial experiment with n = 7 trials where the probability of success on a single trial is p = 0.60. (a) Find P(r = 7). (b) Find P(r ≤ 62 by using the complement rule.
Consider a binomial experiment with n = 6 trials where the probability of success on a single trial is p = 0.85. (a) Find P(r ≤ 1). (b) If you conducted the experiment and got fewer than 2 successes, would you be surprised? Why?
Consider a binomial experiment with n = 6 trials where the probability of success on a single trial is p = 0.20. (a) Find P(0 < r ≤ 22. (b) If you conducted the experiment and got 1 or 2 successes, would you be surprised? Why?
A fair quarter is flipped three times. For each of the following probabilities, use the formula for the binomial distribution and a calculator to compute the requested probability. Next, look up the probability in Table 2 of the Appendix and compare the table result with the computed result. (a)
Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn’t know any of the answers. Assuming that Richard guesses on all 10 questions, find the
The following is based on information taken from The Wolf in the Southwest: The Making of an Endangered Species, edited by David Brown (University of Arizona Press). Before 1918, approximately 55% of the wolves in the New Mexico and Arizona region were male, and 45% were female. However, cattle
The one-time fling! Have you ever purchased an article of clothing (dress, sports jacket, etc.), worn the item once to a party, and then returned the purchase? This is called a one-time fling. About 10% of all adults deliberately do a one-time fling and feel no guilt about it In a group of seven
Sociologists say that 90% of married women claim that their husband’s mother is the biggest bone of contention in their marriages (sex and money are lower-rated areas of contention). Suppose that six married women are having coffee together one morning. What is the probability that: (a) All of
A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tight that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 20 businessmen, all of whom wear ties, what is the
Aldrich Ames is a convicted traitor who leaked American secrets to a foreign power. Yet Ames took routine lie detector tests and each time passed them. How can this be done? Recognizing control questions, employing unusual breathing patterns, biting one’s tongue at the right time, pressing
Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open. Estimate the
Approximately 75% of all marketing personnel are extroverts, whereas about 60% of all computer programmers are introverts. (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts? What is the probability that 5 or more are extroverts? What is the
Are your finances, buying habits, medical records, and phone calls really private? A real concern for many adults is that computers and the Internet are reducing privacy. A survey conducted by Peter D. Hart Research Associates for the Shell Poll was reported in USA Today. According to the survey,
According to the same poll quoted in Problem 24, 53% of adults are concerned that Social Security numbers are used for general identification. For a group of eight adults selected at random, we used Minitab to generate the binomial probability distribution and the cumulative binomial probability
What is the age distribution of patients who make office visits to a doctor or nurse? The following table is based on information taken from the Medical Practice Characteristics section of the Statistical Abstract of the United States.Suppose you are a district manager of a health management
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 symmetry. Consider the section of the
In an experiment, there are n independent trials. For each trial, there are three outcomes: A, B, and C. For each trial, the probability of outcome A is 0.40, the probability of outcome B is 0.50, and the probability of outcome C is 0.10. Suppose there are 10 trials. (a) Can we use the binomial
In a carnival game, there are six identical boxes, one of which contains a prize. A contestant wins the prize by selecting the box containing it. Before each game, the old prize is removed and another prize is placed at random in one of the six boxes. Is it appropriate to use the binomial
According to the college registrar’s office, 40% of students enrolled in an introductory statistics class this semester are freshmen, 25% are sophomores, 15% are juniors, and 20% are seniors. You want to determine the probability that in a random sample of five students enrolled in introductory
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 probabilities of r = 0, 1, 2,
Old Friends Information Service is a California company that is in the business of finding addresses of long-lost friends. Old Friends claims to have a 70% success rate. Suppose that you have the names of six friends for whom you have no addresses and decide to use Old Friends to track them. (a)
The Mountain States Office 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 five automobile insurance liability claims is under study. (a) Make a histogram showing the probability
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 sample. (b) Find the mean
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. Suppose that you are driving a considerable distance on a two-lane highway and are passed by 12 vehicles. (a) Let r be the number of vehicles
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 the probability P(r) of r
Have you ever tried to get out of jury duty? About 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty. If 12 people are called for jury duty: (a) what is the probability that all 12 will be available to serve on the jury? (b) what is the
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. Suppose a neighborhood district in a large city suffers repeated property crimes, not always
We now have the tools to solve the Chapter Focus Problem. In the book Manual: A Guide to the Development and Use of the Myers-Briggs Type Indicators by Myers and McCaulley, it was reported that approximately 45% of all university professors are extroverts. Suppose you have classes with six
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. Suppose you are a news reporter following seven criminal trials. (a) If the trials were in Japan, what is
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 P(r ≥ 1) = 1 –
Consider a binomial experiment with n = 8 trials and p = 0.20. (a) Find the expected value and the standard deviation of the distribution. (b) Would it be unusual to obtain 5 or more successes? Explain. Confirm your answer by looking at the binomial probability distribution table.
Consider a binomial experiment with n = 20 trials and p = 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. Confirm your answer by looking at the binomial probability distribution table.
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 questions: (a) Would
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 symmetrical? What is the expected value of this distribution? Is the
Consider a binomial distribution with n = 5 trials. Use the probabilities given in Table 2 of the Appendix to make histograms showing the probabilities of r = 0, 1, 2, 3, 4, and 5 successes for each of the following. Comment on the skewness of each distribution.(a) The probability of success is p =
Figure 6-6 shows histograms of several binomial distributions with n = 6 trials. Match the given probability of success with the best graph.(a) p = 0.30 goes with graph _________.(b) p = 0.50 goes with graph _________.(c) p = 0.65 goes with graph _________.(d) p = 0.90 goes with graph _________.(e)
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.Let us say you are a market researcher who interviews a random sample of 10 households. (a) Suppose you interview 10 households with
What are the requirements for a probability distribution?
Consumer Reports rated airlines and found that 80% of the flights involved in the study arrived on time (that is, within 15 minutes of scheduled arrival time). Assuming that the on-time arrival rate is representative of the entire commercial airline industry, consider a random sample of 200
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 10. Let r be the number of good grapefruit in a sack.(a) Make a histogram of the probability distribution of r.(b)
The Orchard Café has found that about 5% of the diners who make reservations don’t show up. If 82 reservations have been made, how many diners can be expected to show up? Find the standard deviation of this distribution.
The student government claims that 85% of all students favor an increase in student fees to buy indoor potted plants for the classrooms. A random sample of 12 students produced 2 in favor of the project. What is the probability that 2 or fewer in the sample will favor the project, assuming the
List the criteria for a binomial experiment. What does the random variable of a binomial experiment measure?
For a binomial probability distribution, it is unusual for the number of successes to be less than μ − 2.5σ or greater than μ + 2.5σ. (a) For a binomial experiment with 10 trials for which the probability of success on a single trial is 0.2, is it unusual to have more than five successes?
The Consumer Bankers Association released a report showing the lengths of automobile leases for new automobiles. The results are:(a) Use the midpoint of each class, and call the midpoint of the last class 66.5 months, for purposes of computing the expected lease term. Also find the standard
Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. In the National Park Service Scientific Monograph Series 11, Wolf Ecology and Prey Relationships on Isle Royale, Peterson gives results of many wolf€“moose studies. Of special interest is the
State Farm Insurance studies show that in Colorado, 55% of the auto insurance claims submitted for property damage are submitted by males under 25 years of age. Suppose 10 property damage claims involving automobiles are selected at random. (a) Let r be the number of claims made by males under age
A stationery store has decided to accept a large shipment of ball-point pens if an inspection of 20 randomly selected pens yields no more than two defective pens. (a) Find the probability that this shipment is accepted if 5% of the total shipment is defective. (b) Find the probability that this
According to Harper’s Index, 50% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected. (a) What is the probability that 12 or more are serving time for drug dealing? (b) What is the probability that 7 or fewer are serving time for drug
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.
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 probability that the machine will
“Effect of Helium-Neon Laser Auriculotherapy on Experimental Pain Threshold” is the title of an article in the journal Physical Therapy. In this article, laser therapy is discussed as a useful alternative to drugs in pain management for chronically ill patients. To measure pain threshold, a
Let Î± and Î² be any two constants such that aThe base of the rectangle has length Î² ˆ’ Î± and the height of the rectangle is 1/ ( Î² €“ Î±), so the area of the rectangle is 1. As such, this
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 speakers. The time at which the waves arrive
Look at the normal curve in Figure 7-8 and find Î¼, Î¼ + Ïƒ, and Ïƒ.
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 first one has a larger mean than the second one, must it have a
What percentage of the area under the normal curve lies: (a) To the left of μ? (b) Between μ − σ and μ + σ? (c) Between μ − 3σ and μ + 3σ?
What percentage of the area under the normal curve lies: (a) to the right of μ? (b) between m μ − 2σ and μ + 2σ? (c) to the right of μ + 3σ?
Assuming that the heights of college women are normally distributed with mean 65 inches and standard deviation 2.5 inches, answer the following questions. (a) What percentage of women are taller than 65 inches? (b) What percentage of women are shorter than 65 inches? (c) What percentage of women
The incubation time for Rhode Island Red chicks is normally distributed with a mean of 21 days and standard deviation of approximately 1 day. Look at Figure 7-3 and answer the following questions. If 1000 eggs are being incubated, how many chicks do we expect will hatch: (a) In 19 to 23 days? (b)
At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric people lived in the pueblo. Wood from several excavations gave a mean of (year) 1243 with a standard deviation of 36 years (Bandelier Archaeological Excavation Project:
Fawns between 1 and 5 months old in Mesa Verde National Park have a body weight that is approximately normally distributed with mean Î¼ = 27.2 kilograms and standard deviation Ïƒ = 4.3 kilograms (based on information from The Mule Deer of Mesa Verde National Park, by G. W.
Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean Î¼ = 4.8 and standard deviation Ïƒ = 0.3 (based on information from Diagnostic Tests with Nursing Implications, edited
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 mesa, tree-ring dates (for
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the right of z = 0
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the left of z = 0
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the left of z = −1.32
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the left of z = −0.47
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the left of z = 0.45
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the left of z = 0.72
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the right of z = 1.52
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the right of z = 0.15
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the right of z = −1.22
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. To the right of z = −2.17
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = 0 and z = 3.18
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = 0 and z = −1.93
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = −2.18 and z = 1.34
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = −1.40 and z = 2.03
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = 0.32 and z = 1.92
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = 1.42 and z = 2.17
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = −2.42 and z = −1.77
Sketch the areas under the standard normal curve over the indicated intervals and find the specified areas. Between z = −1.98 and z = −0.03
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)
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)
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)
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)

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