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mathematics
elementary statistics picturing
Elementary Statistics 11th Edition Mario F. Triola - Solutions
It is common for public opinion polls to have a “confidence level” of 95%, meaning that there is a 0.95 probability that the poll results are accurate within the claimed margins of error. If each of the following organizations conducts an independent poll, find the probability that all of them
a. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have identical twins? b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twin boys. What is the probability that she will
a. After having a sonogram, a pregnant woman learns that she will have twins. What is the probability that she will have fraternal twins? b. After studying the sonogram more closely, the physician tells the pregnant woman that she will give birth to twins consisting of one boy and one girl. What is
In Phase I of a clinical trial with gene therapy used for treating HIV, five subjects were treated (based on data from Medical News Today). If 20 people were eligible for the Phase I treatment and a simple random sample of five is selected, how many different simple random samples are possible?
In updated results from a test of MicroSort’s XSORT gender-selection technique, 726 births consisted of 668 baby girls and 58 baby boys (based on data from the Genetics & IVF Institute). Based on these results, what is the probability of a girl born to a couple using MicroSort’s XSORT
In a case in Riverhead, New York, nine different crime victims listened to voice recordings of five different men. All nine victims identified the same voice as that of the criminal. If the voice identifications were made by random guesses, find the probability that all nine victims would select
If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will have one child of each sex? Use the data in the following table. Instead of summarizing observed results, the entries reflect the actual probabilities based on births of twins (based on
Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. The letters BUJOM were included in newspapers on the day this exercise was written. How many ways can the letters of BUJOM be arranged? Identify the correct unscrambling, then determine the
Find P(challenge was made by a man or was not successful).Use the data in the accompanying table, which summarizes challenges by tennis players (based on data reported in USA Today). The results are from the first U.S. Open that used the Hawk-Eye electronic system for displaying an instant replay
Recent developments appear to make it possible for couples to dramatically increase the likelihood that they will conceive a child with the gender of their choice. In a test of a gender-selection method, 3 couples try to have baby girls. If this gender-selection method has no effect, what is the
If a pregnant woman is told that she will give birth to fraternal twins, what is the probability that she will give birth to two girls? Use the data in the following table. Instead of summarizing observed results, the entries reflect the actual probabilities based on births of twins (based on data
Repeat Exercise 25 using these letters: AGGYB.Exercise 25Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. The letters BUJOM were included in newspapers on the day this exercise was written. How many ways can the letters of BUJOM be arranged?
The FAA requires that commercial aircraft used for flying in instrument conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.002. What is the probability that a particular flight will be threatened with the failure of
Groups of five babies are randomly selected. In each group, the random variable x is the number of babies with green eyes (based on data from a study by Dr. Sorita Soni at Indiana University). (The symbol 0+ denotes a positive probability value that is very small.)x
Use the range rule of thumb to identify a range of values containing the usual number of peas with green pods. Based on the result, is it unusual to get only one pea with a green pod? Explain. Refer to the accompanying table, which describes results from eight offspring peas. The random variable
For a binomial distribution with n = 10 and p = 0.5, we should not use the Poisson approximation because the conditions n ≥ 100 and np ≤ 10 are not both satisfied. Suppose we go way out on a limb and use the Poisson approximation anyway. Are the resulting probabilities unacceptable
Based on past results found in the Information Please Almanac, there is a 0.1919 probability that a baseball World Series contest will last four games, a 0.2121 probability that it will last five games, a 0.2222 probability that it will last six games, and a 0.3737 probability that it will last
Based on information from MRINetwork, some job applicants are required to have several interviews before a decision is made. The number of required interviews and the corresponding probabilities are: 1 (0.09); 2 (0.31); 3 (0.37); 4 (0.12); 5 (0.05); 6 (0.05).a. Does the given information describe a
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use Table A-1 to find the probability of x successes given the probability p of success on a given trial.n = 14 x = 4 p = 0.60
In a clinical trial of a drug used to help subjects stop smoking, 821 subjects were treated with 1 mg doses of Chantix. That group consisted of 30 subjects who experienced nausea (based on data from Pfizer, Inc.). The probability of nausea for subjects not receiving the treatment was 0.0124.a.
Based on data from CarMax.com, when a car is randomly selected, the number of bumper stickers and the corresponding probabilities are: 0 (0.824); 1 (0.083); 2 (0.039); 3 (0.014); 4 (0.012); 5 (0.008); 6 (0.008); 7 (0.004); 8 (0.004); 9 (0.004).a. Does the given information describe a probability
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use Table A-1 to find the probability of x successes given the probability p of success on a given trial.n = 10 x = 2 p = 0.05
The Telektronic Company hired 8 employees from a large pool of applicants with an equal number of males and females. If the hiring is done without regard to sex, the numbers of females hired and the corresponding probabilities are as follows: 0 (0.004); 1 (0.031); 2 (0.109); 3 (0.219); 4 (0.273); 5
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use Table A-1 to find the probability of x successes given the probability p of success on a given trial.n = 12 x = 12 p = 0.70
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.n = 12 x = 10 p = 3/4
Mario’s Pizza Parlor has just opened. Due to a lack of employee training, there is only a 0.8 probability that a pizza will be edible. An order for 5 pizzas has just been placed. What is the minimum number of pizzas that must be made in order to be at least 99% sure that there will be 5
Let the random variable x represent the number of girls in a family of four children. Construct a table describing the probability distribution, then find the mean and standard deviation. Is it unusual for a family of four children to consist of four girls?
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.n = 9 x = 2 p = 0.35
A description of a Pew Research Center poll referred to “the random generation of the last two digits of telephone numbers.” Each digit has the same chance of being randomly generated. Construct a table representing the probability distribution for digits randomly generated by computer, find
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.n = 20 x = 4 p = 0.15
The analysis of the leading (first) digits of checks led to the conclusion that companies in Brooklyn, New York, were guilty of fraud. For the purposes of this exercise, assume that the leading digits of check amounts are randomly generated by computer.a. Identify the possible leading digits.b.
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.n = 15 x = 13 p = 1/3
In the Illinois Pick 3 lottery game, you pay 50⊄ to select a sequence of three digits, such as 233. If you select the same sequence of three digits that are drawn, you win and collect $250.a. How many different selections are possible?b. What is the probability of winning?c. If you win, what is
Find the probability that at least 1 of the 5 donors has Group O blood. If at least 1 Group O donor is needed, is it reasonable to expect that at least 1 will be obtained?Refer to the accompanying Minitab display. (When blood donors were randomly selected, 45% of them had blood that is Group O
In New Jersey’s Pick 4 lottery game, you pay 50⊄ to select a sequence of four digits, such as 1332. If you select the same sequence of four digits that are drawn, you win and collect $2788.a. How many different selections are possible?b. What is the probability of winning?c. If you win, what is
Find the probability that at least 3 of the 5 donors have Group O blood. If at least 3 Group O donors are needed, is it very likely that at least 3 will be obtained?Refer to the accompanying Minitab display. (When blood donors were randomly selected, 45% of them had blood that is Group O (based on
Find the probability that all of the 5 donors have Group O blood. Is it unusual to get 5 Group O donors from five randomly selected donors? Why or why not?Refer to the accompanying Minitab display. (When blood donors were randomly selected, 45% of them had blood that is Group O (based on data from
Ten peas are generated from parents having the green yellow pair of genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 10 offspring peas, at least 1 has a green pod. Why does the usual rule for rounding (with three significant
Find the probability that at most 2 of the 5 donors have Group O blood.Refer to the accompanying Minitab display. (When blood donors were randomly selected, 45% of them had blood that is Group O (based on data from the Greater New York Blood Program).) The display shows the probabilities obtained
The brand name of Mrs. Fields (cookies) has a 90% recognition rate (based on data from Franchise Advantage). If Mrs. Fields herself wants to verify that rate by beginning with a small sample of 10 randomly selected consumers, find the probability that exactly 9 of the 10 consumers recognize her
The brand name of McDonald’s has a 95% recognition rate (based on data from Retail Marketing Group). If a McDonald’s executive wants to verify that rate by beginning with a small sample of 15 randomly selected consumers, find the probability that exactly 13 of the 15 consumers recognize the
Kim Hunter has $1000 to invest, and her financial analyst recommends two types of junk bonds. The A bonds have a 6% annual yield with a default rate of 1%. The B bonds have an 8% annual yield with a default rate of 5%. (If the bond defaults, the $1000 is lost.) Which of the two bonds is better?
In the United States, 40% of the population have brown eyes (based on data from Dr. P. Sorita Soni at Indiana University). If 14 people are randomly selected, find the probability that at least 12 of them have brown eyes. Is it unusual to randomly select 14 people and find that at least 12 of them
The Sky Ranch is a supplier of aircraft parts. Included in stock are eight altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected without replacement. Let the random variable x represent the number that are not correctly calibrated. Find the mean and
There is a 1% delinquency rate for consumers with FICO (Fair Isaac & Company) credit rating scores above 800. If the Jefferson Valley Bank provides large loans to 12 people with FICO scores above 800, what is the probability that at least one of them becomes delinquent? Based on that
Assume that you have two blank dice, so that you can label the 12 faces with any numbers. Describe how the dice can be labeled so that, when the two dice are rolled, the totals of the two dice are uniformly distributed in such a way that the outcomes of 1, 2, 3, ... , 12 each have probability 1/12
Ten peas are generated from parents having the green yellow pair of genes, so there is a 0.75 probability that an individual pea will have a green pod. Find the probability that among the 10 offspring peas, at least 9 have green pods. Is it unusual to get at least 9 peas with green pods when 10
The television show NBC Sunday Night Football broadcast a game between the Colts and Patriots and received a share of 22, meaning that among the TV sets in use, 22% were tuned to that game (based on data from Nielsen Media Research). An advertiser wants to obtain a second opinion by conducting its
A medical testing laboratory saves money by combining blood samples for tests, so that only one test is conducted for several people. The combined sample tests positive if at least one person is infected. If the combined sample tests positive, then individual blood tests are performed. In a test
In a survey of 320 college graduates, 36% reported that they stayed on their first full-time job less than one year (based on data from USA Today and Experience.com).a. If 15 of those survey subjects are randomly selected without replacement for a follow-up survey, find the probability that 5 of
In a survey of 150 senior executives, 47% said that the most common job interview mistake is to have little or no knowledge of the company.a. If 6 of those surveyed executives are randomly selected without replacement for a follow-up survey, find the probability that 3 of them said that the most
After being rejected for employment, Jennifer Summer learns that the Kingston Technology Corporation has hired only 3 women among the last 24 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men and women. Help her address the
The Write Right Company manufactures ballpoint pens and has been experiencing a 6% rate of defective pens. Modifications are made to the manufacturing process in an attempt to improve quality. The manager claims that the modified procedure is better because a test of 60 pens shows that only 1 is
The Chapter Problem notes that Mendel obtained 428 peas with green pods when 580 peas were generated. He theorized that the probability of a pea with a green pod is 0.75. If the 0.75 probability value is correct, find the probability of getting 428 peas with green pods among 580 peas. Is that
If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by p(x) = p(1 - p)x-1 where p is the probability of success on any
The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes denoted by A, B, and C. Let P(A) = p1, P(B) = p2, and P(C) = p3. In n independent
What is a normal distribution? What is a standard normal distribution?
Example 4 referred to three randomly selected households in which the numbers of people are 2, 3, and 10. As in Example 4, consider the values of 2, 3, and 10 to be a population and assume that samples of size n = 2 are randomly selected with replacement. Construct a probability distribution table
Less than - 2.75Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celsius degrees.) If
In Example 2, it was noted that a recent Pew Research Center survey showed that among 2822 randomly selected adults, 2060 (or 73%) stated that they are Internet users. A technology specialist claims that 75% of adults use the Internet, and the results from the survey show a lower percentage because
When 3 births are randomly selected, the sample space is bbb, bbg, bgb, bgg, gbb, gbg, ggb, and ggg. Assume that those 8 outcomes are equally likely. Describe the sampling distribution of the proportion of girls from 3 births as a probability distribution table. Does the mean of the sample
A sample of braking distances (in feet) measured under standard conditions for an Acura RL, Acura TSX, Audi A6, BMW 525i, and Buick LaCrosse: 131, 136, 129, 127, 146.Use the given data values to identify the corresponding z scores that are used for a normal quantile plot. Then construct the normal
Find the third quartile Q3, which is the IQ score separating the top 25% from the others.Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Less than 1.23Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celsius degrees.) If using
The Genetics & IVF Institute developed its XSORT method to increase the probability of conceiving a girl. Among 574 women using that method, 525 had baby girls. Assuming that the method has no effect so that boys and girls are equally likely, find the probability of getting at least 525 girls
A sample of the numbers of satellites in orbit: 158 (United States); 17 (China); 18 (Russia); 15 ( Japan); 3 (France); 5 (Germany).Use the given data values to identify the corresponding z scores that are used for a normal quantile plot. Then construct the normal quantile plot and determine whether
Greater than 2.22Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celsius degrees.) If
Less than 2.34Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celsius degrees.) If using
The Genetics & IVF Institute developed its YSORT method to increase the probability of conceiving a boy. Among 152 women using that method, 127 had baby boys. Assuming that the method has no effect so that boys and girls are equally likely, find the probability of getting at least 127 boys
The Mark VI monorail used at Disney World and the Boeing 757-200 ER airliner have doors with a height of 72 in.a. What percentage of adult men can fit through the doors without bending?b. What percentage of adult women can fit through the doors without bending?c. Does the door design with a height
When Mendel conducted his famous hybridization experiments, he used peas with green pods and yellow pods. One experiment involved crossing peas in such a way that 25% (or 145) of the 580 offspring peas were expected to have yellow pods. Instead of getting 145 peas with yellow pods, he obtained 152.
The following values are the times (in days) it took for prototype integrated circuits to fail. Test these values for normality, then replace each x value with log (x + 1) and test the transformed values for normality. What can you conclude? 103 547 106 662 329 510 1169 267 1894 1065 1396 307 362
Greater than 2.33Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celsius degrees.) If
Tall Clubs International is a social organization for tall people. It has a requirement that men must be at least 74 in. tall, and women must be at least 70 in. tall.a. What percentage of men meet that requirement?b. What percentage of women meet that requirement?c. Are the height requirements for
Find P30, which is the IQ score separating the bottom 30% from the top 70%.Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Greater than - 1.75Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celsius degrees.) If
Tall Clubs International has minimum height requirements for men and women.a. If the requirements are changed so that the tallest 4% of men are eligible, what is the new minimum height for men?b. If the requirements are changed so that the tallest 4% of women are eligible, what is the new minimum
Greater than -1.96Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celsius degrees.) If
The U.S. Army requires women’s heights to be between 58 in. and 80 in.a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join the Army because they are too short or too tall?b. If the U.S. Army changes the height requirements so that all
Find the mean, median, and standard deviation. Use the following weights (in pounds) of randomly selected supermodels. 125 (Taylor) 119 (Auermann) 128 (Schiffer) 125 (Bundchen) 119 (Turlington) 127 (Hall) 105 (Moss) 123 (Mazza) 110 (Reilly) 103 (Barton)
A “snapshot” in USA Today noted that “Consumers will spend an estimated average of $483 on merchandise” for back-to-school spending. It was reported that the value is based on a survey of 8453 consumers, and the margin of error is “±1 percentage point.” What’s wrong with this
USA Today provided a “snapshot” illustrating poll results from 21,944 subjects. The illustration showed that 43% answered “yes” to this question: “Would you rather have a boring job than no job?” The margin of error was given as ± 1 percentage point. What important feature of the poll
Quest Diagnostics is a provider of drug testing for job applicants, and its managers want to estimate the proportion of job applicants who test positive for drugs. In this context, what is a point estimate of that proportion? What is a confidence interval? What is a major advantage of the
In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Construct a 95% confidence interval estimate of the percentage of all adults who have that belief, and then write a statement interpreting the confidence
See the survey described in Exercise 1. Assume that you must conduct a new poll to determine the percentage of adults who believe that it is morally wrong to not report all income on tax returns. How many randomly selected adults must you survey if you want 99% confidence that the margin of error
What is the level of measurement of these data (nominal, ordinal, interval, ratio)? Use the following weights (in pounds) of randomly selected supermodels. 125 (Taylor) 119 (Auermann) 128 (Schiffer) 125 (Bundchen) 119 (Turlington) 127 (Hall) 105 (Moss) 123 (Mazza) 110 (Reilly) 103 (Barton)
A design engineer for the Ford Motor Company must estimate the mean leg length of all adults. She obtains a list of the 1275 employees at her facility, then obtains a simple random sample of 50 employees. If she uses this sample to construct a 95% confidence interval to estimate the mean leg length
What does it mean when we say that the methods for constructing confidence intervals in this section are robust against departures from normality? Are the methods for constructing confidence intervals in this section robust against poor sampling methods?
Is the confidence interval given in Exercise 1 equivalent to the expression (0.0455 g, 0.0602 g)? Is the confidence interval given in Exercise 1 equivalent to the expression 0.05285 g ± 0.00735 g? Why or why not?
Here is a 95% confidence interval estimate of the proportion of all job applicants who test positive when they are tested for drug use: 0.0262 < p < 0.0499 (based on data from Quest Diagnostics). Write a statement that correctly interprets this confidence interval.
See the survey described in Exercise 1. Assume that you must conduct a survey to determine the mean income reported on tax returns, and you have access to actual tax returns. How many randomly selected tax returns must you survey if you want to be 99% confident that the mean of the sample is within
Based on the heights of women listed in Data Set 1 in Appendix B, and assuming that heights of women have a standard deviation of ? = 2.5 in., this 95% confidence interval is obtained: 62.42 in. .01 .05 .10 .20 .30 .40 .50 .60 .70 .80 .90 .95 .99 .914 630 387 .134 .040 .010 .002 0+ O+ O+ O+ 0+
For the poll described in Exercise 1, we see that 43% of 21,944 people polled answered “yes” to the given question. Given that 43% is the best estimate of the population percentage, why would we need a confidence interval? That is, what additional information does the confidence interval
A pollster for the Gallup Organization randomly generates the last two digits of telephone numbers to be called, so the numbers from 00 to 99 are all equally likely. Can the methods of this section be used to construct a confidence interval estimate of the standard deviation of the population of
What is the confidence level of the confidence interval given in Exercise 2? What is a confidence level in general?Exercise 2Here is a 95% confidence interval estimate of the proportion of all job applicants who test positive when they are tested for drug use: 0.0262 < p < 0.0499 (based on
A simple random sample of 37 weights of pennies made after 1983 has a mean of 2.4991 g and a standard deviation of 0.0165 g (based on Data Set 20 in Appendix B). Construct a 99% confidence interval estimate of the mean weight of all such pennies. Design specifications require a population mean of
Find the sample size necessary to estimate the mean weight of all supermodels so that there is 95% confidence that the sample mean is in error by no more than 2 lb. Assume that a pilot study suggests that the weights of all supermodels have a standard deviation of 7.5 lb. Use the following weights
One of the features of the sample mean that makes it a good estimator of a population mean μ is that the sample mean is an unbiased estimator. What does it mean for a statistic to be an unbiased estimator of a population parameter?
A simple random sample of size n = 5 is obtained from the population of drivers living in New York City, and the braking reaction time of each driver is measured. The results are to be used for constructing a 95% confidence interval. What is the number of degrees of freedom that should be used for
Suppose the poll results from Exercise 1 were obtained by mailing 100,000 questionnaires and receiving 21,944 responses. Is the result of 43% a good estimate of the population percentage of “yes” responses? Why or why not?
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