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mathematics
elementary statistics picturing

Questions and Answers of Elementary Statistics Picturing

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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?
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
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
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:
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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?
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
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
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.
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
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
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
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
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
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
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
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”

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