STATS Homework questions, Chapter 3 and 4, Chapter 5 and 6, Chapter 7

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Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. area = .9838

2.14 = z score

Find the third quartile Q3 of the list of 24 sorted values shown below. 30 31 32 32 36 40 41 47 47 49 52 53 54 55 56 59 61 62 64 64 68 71 78 80 A. 62.5 Your answer is correct.B. 68

62.5

Which of the following is not true?

A z-score is an area under the normal curve.

The population of current statistics students has ages with mean muμ and standard deviation sigmaσ. Samples of statistics students are randomly selected so that there are exactly 4949 students in each sample. For each sample, the mean age is computed. What does the central limit theorem tell us about the distribution of those mean ages?

Because ngreater than>30, the sampling distribution of the mean ages can be approximated by a normal distribution with mean muμ and standard deviation StartFraction sigma Over StartRoot 49 EndRoot EndFraction σ 49.

To determine customer opinion of their safety featuressafety features, ToyotaToyota randomly selects 150150 dealershipsdealerships during a certain week and surveys all customers visiting the dealershipscustomers visiting the dealerships.

Cluster

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A manman experienced a tax audit. The tax department claimed that the manman was audited because everyoneeveryone inin sixsix randomlyrandomly selectedselected districtsdistricts waswas beingbeing audited.audited. nothing nothing nothing Which type of sampling did the tax department use?

Cluster Sample

The definition of "Census" is a

Collection of data from every member of a population

A _______ random variable has infinitely many values associated with measurements.

Continuous

Determine whether the value is from a discrete or continuous data set. Number of members present at a meeting is 6Number of members present at a meeting is 6 Is the value from a discrete or continuous data set?

Discrete

Determine whether the value is from a discrete or continuous data set. Number of pieces of lumber used to make a deck is 113Number of pieces of lumber used to make a deck is 113

Discrete

Events that are _______ cannot occur at the same time.

Disjoint

Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. x 0 1 2 3 4 5 P(x) 0.00140.0014 0.01940.0194 0.10490.1049 0.28360.2836 0.38340.3834 0.20730.2073

Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. muμequals= 3.7 Find the standard deviation of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. equals= 1.01.0

the Heights of the bars of a histogram correspond to ____ values.

Frequency. A histogram is a graph consisting of bars of equal width drawn adjacent to each other (without gaps). The horizontal scale represents classes of quantitative data values and the vertical scale represents frequencies. The heights of the bars correspond to the frequency values.

The measure of center that is the value that occurs with the greatest frequency is the _______.

Mode

Decide whether the following two events are disjoint. 1. Electing a president of the United StatesElecting a president of the United States 2. Electing a female candidateElecting a female candidate

NoNo, because the events cancan occur at the same time.

Which measure of variation is very sensitive to extreme values?

Range

The Definition of a "Sample" is a

Subcollection of members selected from a population

For data sets having a distribution that is approximately bell-shaped, _______ states that about 68% of all data values fall within one standard deviation from the mean.

The Empirical Rule

The probability of an event that is certain to occur is 1.

This is a principle of probability.

A z-score is a conversion that standardizes any value from a normal distribution to a standard normal distribution.

True

Complete the following statement. If you are asked to find the 85th percentile, you are being asked to find _____.

a data value associated with an area of 0.85 to its left

A _______ random variable has either a finite or a countable number of values.

discrete

The _______ of a discrete random variable represents the mean value of the outcomes

expected value

Finding probabilities associated with distributions that are standard normal distributions is equivalent to _______.

finding the area of the shaded region representing that probability.

A(n) frequency polygon uses line segments to connect points located directly above class midpoint values.

frequency polygon

Selections made with replacement are considered to be _______.

independent

Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.

independent

Which measure of center is sensitive to extreme values?

mean

The square of the standard deviation is called the _______.

variance

If P(A)equals=0.9960.996, what is the value of P(Upper A overbarA)?

P(Upper A overbarA)equals= . 004.004 (Type an integer or a decimal.)

Assume the readings on thermometers are normally distributed with a mean of 0degrees°C and a standard deviation of 1.00degrees°C. Find the probability that a randomly selected thermometer reads greater than 2.082.08 and draw a sketch of the region.

.0188

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.\ 70

.0228

Assume the readings on thermometers are normally distributed with a mean of 0degrees°C and a standard deviation of 1.00degrees°C. Find the probability Upper P left parenthesis z less than minus 2.16 or z greater than 2.16 right parenthesisP(z<−2.16 or z>2.16), where z is the reading in degrees.

.0308

Assume the readings on thermometers are normally distributed with a mean of 0degrees°C and a standard deviation of 1.00degrees°C. Find the probability that a randomly selected thermometer reads between negative 2.12−2.12 and negative 1.61−1.61 and draw a sketch of the region.

.0367

Assume that adults have IQ scores that are normally distributed with a mean of 105105 and a standard deviation of 15. Find the third quartile Upper Q 3Q3, which is the IQ score separating the top 25% from the others.

115.1

Determine whether the value given below is from a discrete or continuous data set. The volume of cola in a can is 11.5 oz.The volume of cola in a can is 11.5 oz. nothing nothing nothing nothing nothing nothing nothing Choose the correct answer below.

A continuouscontinuous data set because there are infinitely many possible values and thosethere are infinitely many possible values and those values cannot be counted

Determine whether the value given below is from a discrete or continuous data set. The volume of cola in a can is 11.6 oz.The volume of cola in a can is 11.6 oz. nothing nothing nothing nothing nothing nothing nothing Choose the correct answer below.

A continuouscontinuous data set because there are infinitely many possible values and thosethere are infinitely many possible values and those values cannot be counted

Determine whether the value given below is from a discrete or continuous data set. In a test of a method of gender selection comma 690 couples used the XSORT methodIn a test of a method of gender selection, 690 couples used the XSORT method andand 544544 ofof themthem hadhad babybaby girls.girls. Choose the correct answer below.

A discretediscrete data set because there are a finite number of possible valuesthere are a finite number of possible values

Which of the following is associated with a parameter?

A parameter is a numerical measurement describing some characteristic of a population. So, a parameter is associated with data that were obtained from an entire population.

What is a voluntary response sample?

A sample in which the subjects themselves decide whether to be included in the study. A voluntary response sample is one in which the subjects themselves decide whether to be included in the study.

About _____% of the area is between zequals=negative 1.6−1.6 and zequals=1.61.6 (or within 1.61.6 standard deviationsdeviations of the mean).

About 89.0489.04% of the area is between zequals=negative 1.6−1.6 and zequals=1.61.6 (or within 1.61.6 standard deviationsdeviations of the mean).

When using the _______ always be careful to avoid double-counting outcomes.

Addition rule

Which of the following is NOT a principle of probability?

All events are equally likely in any probability procedure.

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A manman experienced a tax audit. The tax department claimed that the manman was audited because hehe waswas randomlyrandomly selectedselected fromfrom allall thethe taxpayers.taxpayers. nothing nothing nothing nothing Which type of sampling did the tax department use?

Random sampling

Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. Upper A magazineA magazine asks its readersreaders to call in their opinion regarding the quality of thethe quality of the articles.articles. Which type of sampling is used?

Connivence

Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. Upper A television stationA television station asks its viewersviewers to call in their opinion regarding the variety ofthe variety of sports programming.

Connivence

Determine whether the value is from a discrete or continuous data set. Frequency of a guitar note is 430 HzFrequency of a guitar note is 430 Hz Is the value from a discrete or continuous data set?

Continuous

Determine whether the value is from a discrete or continuous data set. Time to learn a song is 4 hoursTime to learn a song is 4 hours Is the value from a discrete or continuous data set?

Continuous

Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. An internet siteAn internet site asks its membersmembers to call in their opinion regarding their reluctancetheir reluctance to provide credit information online.to provide credit information online. Which type of sampling is used?

Convenience

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. In a poll conducted by a certain research center, 12091209 adults were called after their telephone numbers were randomly generated by a computer, and 3 %3% were able to correctly identify the secretary of state.secretary of state. Which type of sampling did the research center use?

Random sampling

There is a 0.05310.0531 probability that a best-of-seven contest will last four games, a 0.11860.1186 probability that it will last five games, a 0.28090.2809 probability that it will last six games, and a 0.54740.5474 probability that it will last seven games. Verify that this is a probability distribution. Find its mean and standard deviation.

Mean = 6.32 SD = .88

youryour oddsodds ofof carcar thefttheft byby nbsp 300 percent." 300 percent." What is wrong with this statement?

Misleading

Determine whether the given value is a statistic or a parameter. In a study of all 1294 students at a college comma it is found that 45 % own a television.In a study of all 1294 students at a college, it is found that 45% own a television. Choose the correct statement below.

Parameter because the value is a numerical measurement describing a characteristic of a populationpopulation.

Determine whether the given value is a statistic or a parameter. In a study of all 3336 seniors at a college comma it is found that 55 % own a vehicle.In a study of all 3336 seniors at a college, it is found that 55% own a vehicle. Choose the correct statement below.

Parameter because the value is a numerical measurement describing a characteristic of a populationpopulation.

Determine whether the given value is a statistic or a parameter. In a study of all 1452 students at a college comma it is found that 45 % own a computer.In a study of all 1452 students at a college, it is found that 45% own a computer. Choose the correct statement below.

ParameterParameter because the value is a numerical measurement describing a characteristic of a populationpopulation.

Determine whether the given value is a statistic or a parameter. In a study of all 4171 professors at a college comma it is found that 45 % own a television.

ParameterParameter because the value is a numerical measurement describing a characteristic of a populationpopulation.

Probability is .3409

Which of the following is NOT a level of measurement?

Quantitative refers to a data type, not a level of measurement.

Choose the correct answer below

Quiz scores from a college level statistics course are analyzed to determine student progress. Using quiz scores from a college level statistics course that are analyzed to determine student progress would not be a voluntary response sample because respondents themselves do not decide to be included.

A _______ variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure.

Random

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. In a poll conducted by a certain research center, 900900 adults were called after their telephone numbers were randomly generated by a computer, and 20 %20% were able to correctly identify the president.president. Which type of sampling did the research center use?

Random sampling

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. In a poll conducted by a certain research center, 911911 adults were called after their telephone numbers were randomly generated by a computer, and 55 %55% were able to correctly identify the president.president. Which type of sampling did the research center use?

Random sampling

Which measure of variation is very sensitive to extreme values? Choose the correct answer below.

Range

Use the given information to find the minimum sample size required to estimate an unknown population mean muμ. How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 9090% confidence that the sample mean is within 22 points of the population mean, and the population standard deviation is 6262.

The minimum sample size required is 2,6012,601 adults.

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. .85 = area

The indicated IQ score, x, is 115.6115.6

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

The indicated IQ score, x, is 71.871.8.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Years in which an Olympics was heldYears in which an Olympics was held Choose the correct answer below.

The intervalinterval level of measurement is most appropriate because the data can becan be ordered commaordered, differences left parenthesis obtained by subtraction right parenthesisdifferences (obtained by subtraction) can becan be foundfound and areand are meaningful commameaningful, and thereand there is nois no naturalnatural startingstarting zerozero point.

Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. nbsp 95 % confidence; the sample size is 1033 comma of which 40 % are successes

The margin of error Eequals= 0.02990.0299

Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. n equals 500 comma x equals 150 comma 95 % confidencen=500, x=150, 95% confidence

The margin of error Eequals= 0.04020.0402.

Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. n equals 550 comma x equals 330 comma 95 % confidence

The margin of error Eequals= 0.04090.0409.

Listed below are the measured radiation emissions (in W/kg) corresponding to cell phones: A, B, C, D, E, F, G, H, I, J, and K respectively. The media often present reports about the dangers of cell phone radiation as a cause of cancer. Cell phone radiation must be 1.6 W/kg or less. Find the a. mean, b. median, c. midrange, and d. mode for the data. Also complete part e.

The maximum data value is the most relevant statistic, because it is closest to the limit of 1.6W/kg and that cell phone should be avoided.

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

The mean and standard deviation have the values of mu equals 0μ=0 and sigma equals 1.

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below.

The mean and standard deviation have the values of mu equals 0μ=0 and sigma equals 1.

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?

The mean and standard deviation have the values of mu equals μ=0 and sigma equals σ=1.

Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data in millions of dollars. Given that these are the top 10 salaries, do we know anything about the salaries of TV personalities in general? Are such top 10 lists valuable for gaining insight into the larger population? 38.938.9 36.936.9 34.734.7 27.927.9 14.914.9 12.812.8 11.711.7 10.510.5 9.39.3 9.19.1 Given that these are the top 10 salaries, do we know anything about the salaries of TV personalities in general? Are such top 10 lists valuable for gaining insight into the larger population?

The mean is 20.67 The median is 13.85 No Mode Midrange is 24 Since the sample values are the 10 highest, they give almost no information about the salaries of TV personalities in general. No, because such top 10 lists represent an extreme subset of the population rather than the larger population

Which of the following is NOT a characteristic of the mean?

The mean is called the average by statisticians.

Which level of measurement consists of categories only where data cannot be arranged in an ordering scheme?

The nominal level of measurement is characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme (such as low to high).

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Types of restaurants left parenthesis fast food comma organic food comma sea food comma etc. right parenthesisTypes of restaurants (fast food, organic food, sea food, etc.) Choose the correct answer below.

The nominalnominal level of measurement is most appropriate because data cannotdata cannot be arrangedbe arranged in an ordering schemein an ordering scheme.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Flight numbers

The nominalnominal level of measurement is most appropriate because the data cannotcannot bebe ordered.ordered. nothing nothing nothing nothing nothing nothing nothing nothing nothing

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Car models

The nominalnominal level of measurement is most appropriate because the data cannotcannot bebe ordered.ordered. nothing nothing nothing nothing nothing nothing nothing nothing nothing nothing

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Types of movies left parenthesis drama comma comedy comma adventure comma documentary comma etc. right parenthesisTypes of movies (drama, comedy, adventure, documentary, etc.) Choose the correct answer below.

The nominalnominal level of measurement is most appropriate because the data cannotcannot bebe ordered.ordered. nothing nothing nothing nothing nothing nothing nothing nothing nothing nothing

Which of the following consists of discrete data?

The number of suitcases on a plane is a number representing a count. This would consist of discrete data.

Conclusion of Central Limit Theorem

The mean of all sample means is the population mean muμ. The distribution of the sample means x overbarx will, as the sample size increases, approach a normal distribution. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample size.

The probability is 0.98260.9826.

Listed below are the numbers of manatee deaths caused each year by collisions with watercraft. The data are listed in order for each year of the past decade. Find the range, variance, and standard deviation of the data set. What important feature of the data is not revealed through the different measures of variation?

The measures of variation reveal nothing about the pattern over time.

Listed below are the amounts of mercury (in parts per million, or ppm) found in tuna sushi sampled at different stores. Find the range, variance, and standard deviation for the set of data. What would be the values of the measures of variation if the tuna sushi contained no mercury?

The measures of variation would all be 0.

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 105μ=105 and a standard deviation sigma equals 20σ=20. Find the probability that a randomly selected adult has an IQ between 8787 and 123123.

The probability that a randomly selected adult has an IQ between 8787 and 123123 is 0.63190.6319.

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100μ=100 and a standard deviation sigma equals 15σ=15. Find the probability that a randomly selected adult has an IQ between 9090 and 110110.

The probability that a randomly selected adult has an IQ between 9090 and 110110 is . 4972.4972.

Assume that adults have IQ scores that are normally distributed with a mean of mu equals 100μ=100 and a standard deviation sigma equals 20σ=20. Find the probability that a randomly selected adult has an IQ between 9090 and 110110.

The probability that a randomly selected adult has an IQ between 9090 and 110110 is 0.38290.3829.

Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Surveying 100 married individuals and recording if they have ever been divorcedSurveying 100 married individuals and recording if they have ever been divorced nothing

Yes because there are more than two possible outcomes

Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.210.21 1 0.280.28 2 0.020.02 3 0.280.28 4

Yes, Because the probabilities sum to 1 and are all between 0 and 1 inclusive

Listed below are the durations (in hours) of a simple random sample of all flights of a space shuttle program. Find the range, variance, and standard deviation for the sample data. Is the lowest duration time unusual? Why or why not?

Yes, because it is more than two standard deviations below the mean.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administered to 120120 randomly selected individuals, with the number of individuals responding favorably recorded.

Yes, because the experiment satisfies all the criteria for a binomial experiment.

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. In a poll conducted by a certain research center, 793793 adults were called after their telephone numbers were randomly generated by a computer, and 83 %83% were able to correctly identify the president.president. Which type of sampling did the research center use?

Random sampling

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. In a poll conducted by a certain research center, 894894 adults were called after their telephone numbers were randomly generated by a computer, and 9 %9% were able to correctly identify the secretary of state.secretary of state. Which type of sampling did the research center use?

Random sampling

Whenever a data value is less than the mean,

the corresponding z-score is negative.

Whenever a data value is less than the mean, _______.

the corresponding z-score is negative.

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. area = .9

x = 80.8

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. z = 0.75

x = 89.9

Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. z = .65

x = 94.2

If P(A)equals=0.9960.996, is Upper A overbarA unlikely?

yes

Do one of the following, as appropriate. (a) Find the critical value z Subscript alpha divided by 2zα/2, (b) find the critical value t Subscript alpha divided by 2tα/2, (c) state that neither the normal nor the t distribution applies. Confidence level 9090%; nequals=1616; sigma equals 19.9σ=19.9; population appears to be normally distributednormally distributed.

z = 1.645

When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a _______.

z-score

When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a _______.

z-scores

Find the critical value z Subscript alpha divided by 2zα/2 that corresponds to the given confidence level. 9797%

z= 2.17

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administered to 5050 randomly selected individuals, with the number of individuals responding favorably recorded.

Yes, because the experiment satisfies all the criteria for a binomial experiment.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administered to 200200 randomly selected individuals, with the number of individuals responding favorably recorded. Does the probability experiment represent a binomial experiment?

Yes, because the experiment satisfies all the criteria for a binomial experiment.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administered to 6060 randomly selected individuals, with the number of individuals responding favorably recorded.

Yes, because the experiment satisfies all the criteria for a binomial experiment.

In a study of a weight loss program, 4545 subjects lost a mean of 3.13.1 lbs after 12 months. Methods of statistics can be used to show that if this diet had no effect, the likelihood of getting these results is roughly 1010 chances in 1000. Does the weight loss program have statistical significance? Does the weight loss program have practical significance?

Yes, because the results are unlikely to occur by chance. No, someone starting a weight loss program would likely want to lose considerably more than 2.42.4 lb.

Do the second and third alarm clocks result in greatly improved reliability?

Yes, because total malfunction would not be impossible, but it would be unlikely.

Is there a duration time that is very unusual? How might that duration time be explained?

Yes, the time of 0 hours is very unusual. It could represent a flight that was aborted.

Statistics are sometimes used to compare or identify authors of different works. The lengths of the first 10 words in a book by Terry are listed with the first 10 words in a book by David. Find the mean and median for each of the two samples, then compare the two sets of results.

Yes. Based on the results, words in Terry's book are longer thanlonger than the words in David's book.

Listed below are the playing times (in seconds) of songs that were popular at the time of this writing. Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. Is there one time that is very different from the others? Is there one time that is very different from the others?

Yes; the time of 443443 seconds is very different from the others.

Determine whether the value is from a discrete or continuous data set. Amount of fabric needed for a dress is 2.5 ydsAmount of fabric needed for a dress is 2.5 yds Is the value from a discrete or continuous data set?

You answered DiscreteDiscrete. The correct answer is ContinuousContinuous because the value for the "amount of fabric needed for a dress""amount of fabric needed for a dress" is one of infinitely many possibleone of infinitely many possible valuesvalues and thoseand those values cannot be counted.

If you are asked to find the 85th percentile, you are being asked to find _____.

a data value associated with an area of 0.85 to its left

f you are asked to find the 85th percentile, you are being asked to find _____.

a data value associated with an area of 0.85 to its left

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

he area of the shaded region is 0.5557

Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping.") Randomly selecting someone who plays footballfootball. Randomly selecting someone taking a statisticsstatistics course. Choose the correct answer below.

he events are not disjoint. They can occur at the same time.

During a period of 11 years 14601460 of the people selected for grand jury duty were sampled, and 3535% of them were immigrants. Use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. Given that among the people eligible for jury duty, 59.359.3% of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants?

Yes, the confidence interval does not includedoes not include the true percentage of immigrants.

In the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation. x P(x) 0 0.040.04 1 0.110.11 2 0.260.26 3 0.320.32 4 0.160.16 5

mean = 2.8 SD 1.3

A candy company claims that 1212% of its plain candies are orange, and a sample of 200200 such candies is randomly selected.

mean = 24 SD = 4.6

Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. x 0 1 2 3 4 5 P(x) 0.00000.0000 0.00070.0007 0.01050.0105 0.08530.0853 0.34510.3451 0.55840.5584

mean = 4.5 SD = 0.7

A value at the center or middle of a data set is a(n) _______.

measure of center

A candy company claims that 2121% of its plain candies are orange, and a sample of 200200 such candies is randomly selected.

mu = 42 sigma = 5.8

There is a 0.10710.1071 probability that a best-of-seven contest will last four games, a 0.16990.1699 probability that it will last five games, a 0.29620.2962 probability that it will last six games, and a 0.42680.4268 probability that it will last seven games. Verify that this is a probability distribution. Find its mean and standard deviation.

mu = 6.04 Sigma = 1.01

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: fourfour percentage points; confidence level 9090%; from a prior study, ModifyingAbove p with caretp is estimated by the decimal equivalent of 3434%

n=380

An IQ test is designed so that the mean is 100 and the standard deviation is 2020 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 9090% confidence that the sample mean is within 77 IQ points of the true mean. Assume that sigmaσequals=2020 and determine the required sample size.

nequals= 2323

Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: 0.060.06; confidence level 9595%; ModifyingAbove p with caretp and ModifyingAbove q with caretq unknown

nequals= 267267

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. States in a regionStates in a region Choose the correct level of measurement.

nominal

Identify the expression for calculating the mean of a binomial distribution.

In the binomial probability formula, the variable x represents the _______.

number of successes

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Positions of runners in a racePositions of runners in a race Choose the correct level of measurement.

ordinal

Assume that a procedure yields a binomial distribution with nequals=66 trials and a probability of success of pequals=0.600.60. Use a binomial probability table to find the probability that the number of successes x is exactly 11.

p (1) = .037

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. nequals=9, xequals=4, pequals=0.45

p (4) = .26

p (4) = .263

ssume 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. nequals=19, xequals=15, pequals=0.85

p(15) = .171

Which of the following values cannot be probabilities? 0.060.06, negative 0.5−0.5, StartRoot 2 EndRoot2, 3 divided by 53/5, 11, 1.581.58, 00, 5 divided by 3

rad 2 5/3 1.58 -0.5

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Voltage measurements of batteries: 1.5 Upper V comma 3 Upper V comma 4.5 Upper V comma 6 Upper V comma and 7.5 Upper VVoltage measurements of batteries: 1.5 V, 3 V, 4.5 V, 6 V, and 7.5 V Choose the correct answer below.

ratio

A certain group of women has a 0.070.07% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?

,9993

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z= .72

The area of the shaded region is 0.76420.7642.

.0166

Ted is not particularly creative. He uses the pickup line "If I could rearrange the alphabet, I'd put U and I together." The random variable x is the number of girls Ted approaches before encountering one who reacts positively. Determine whether the table describes a probability distribution. If it does, find its mean and standard deviation. x P(x) 1 0.0010.001 2 0.0170.017 3 0.1050.105 4 0.2020.202 5 0.4500.450

- not a probability distribution

Which of the following values cannot be probabilities? 11, 5 divided by 35/3, 3 divided by 53/5, negative 0.56−0.56, StartRoot 2 EndRoot2, 1.331.33, 00, 0.04

-0.56 rad2 5/3 1.33

. 8962

wo cards are randomly selected without replacement from a shuffled deck of cards. Find the probability of getting an ace on the first draw and an ace on the second draw.

.004525

Two cards are randomly selected WITH replacement from a shuffled deck of cards. Find the probability of getting an ace on the first draw and an ace on the second draw.

.005917

.0132

.0150

he accompanying table contains the results from experiments with a polygraph instrument. Find the probabilities of the events in parts (a) and (b) below. Are these events unlikely? a. Four of the test subjects are randomly selected with replacement, and they all had true negative test results. b. Four of the test subjects are randomly selected without replacement, and they all had true negative test results.

.047 yes, because the probability of the event is lessless than 0.05. .044 yes, because the probability of the event is lessless than 0.05.

.0764

The table below summarizes results from a study of people who refused to answer survey questions. A pharmaceutical company is interested in opinions of the elderly. What is the probability that the selected subject is someone 60 and over who responded? Age 18-21 22-29 30-39 40-49 50-59 60 and over Responded 7474 256256 246246 137137 139139 203203 Refused 1111 2020 3333 2626 3535 57

.164

Assume the readings on thermometers are normally distributed with a mean of 0degrees°C and a standard deviation of 1.00degrees°C. Find the probability that a randomly selected thermometer reads between negative 2.29−2.29 and negative 0.75−0.75 and draw a sketch of the region.

.2156

The psychologypsychology test score is relatively better because its z score is greater than the z score for the economicseconomics test score.

.25

.2843

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 9191 people in the 18-21 age bracket and finds that 7676 of them respond and 1515 refuse to respond. When 264264 people in the 22-29 age bracket are contacted, 249249 respond and 1515 refuse to respond. Suppose that one of the 355355 people is randomly selected. Find the probability of getting someone in the 18 dash 2118-21 age bracket or someone who refused to respondrefused to respond.

.299

The table below summarizes results from a study of people who refused to answer survey questions. A market researcher is not interested in refusals or subjects below 22 years of age or over 59. Find the probability that the selected person refused to answer or is below 22 or is older than 59. Age 18-21 22-29 30-39 40-49 50-59 60 and over Responded 8080 262262 252252 143143 145145 209209 Refused 1515 2424 3737 3030 3939 6161

.382

he following data lists the number of correct and wrong dosage amounts calculated by 3636 physicians. In a research experiment, a group of 1818 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 1818 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution." If one of the physicians is randomly selected, what is the probability of getting one who calculated the dose correctly? Is that probability as high as it should be?

.5 No. One would want this probability to be very high.

.5478

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z= .38

.6480

Use the data in the following table, which summarizes results from 169169 pedestrian deaths that were caused by accidents. If two different deaths are randomly selected without replacement, find the probability that they both involved intoxicated drivers. Pedestrian Intoxicated? Yes No Driver Yes 120120 2424 Intoxicated? No 2020 55

.7253

Assume the readings on thermometers are normally distributed with a mean of 0degrees°C and a standard deviation of 1.00degrees°C. Find the probability Upper P left parenthesis negative 1.55 less than z less than 1.55 right parenthesisP(−1.55<z<1.55), where z is the reading in degrees.

.8788

The table below summarizes results from a study of people who refused to answer survey questions. A market researcher is interested in responses, especially from those between the ages of 22 and 39. Find the probability that a selected subject responds or is between the ages of 22 and 39. Age 18-21 22-29 30-39 40-49 50-59 60 and over Responded 8080 262262 252252 143143 145145 209209 Refused 1111 2020 3333 2626 3535 5757

.899

.9535

Find the indicated complement. A certain group of women has a 0.730.73% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness? What is the probability that the woman selected does not have red/green color blindness?

.9927

0.0192

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals 500 comma x equals 100 comma 95 % confidence

0.1650.165less than<pless than< 0.2350.235

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 548548 babies were born, and 274274 of them were girls. Use the sample data to construct a 9999% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?

0.4450.445less than< pless than< 0.5550.555 No, the proportion of girls is notis not significantly different from 0.5.

Use the sample data and confidence level to construct the confidence interval estimate of the population proportion p. n equals 600 comma x equals 360 comma 95 % confidencen=600, x=360, 95% confidence

0.5610.561less than<pless than< 0.6390.639

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 300300 babies were born, and 270270 of them were girls. Use the sample data to construct a 9999% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?

0.8550.855less than< pless than< 0.9450.945 (Round to three decimal places as needed.) Does the method appear to be effective? YesYes, the proportion of girls isis significantly different from 0.5.

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 94P94, the 94 th94th percentile. This is the temperature reading separating the bottom 94 %94% from the top 6 %.

1.56

The histogram to the right represents the weights (in pounds) of members of a certain high-school debatedebate team. How many team members are included in the histogram? A histogram has a horizontal axis labeled from less than 110 to 170 plus in intervals of 10 and a vertical axis labeled from 0 to 6 in intervals of 1. Vertical bars, 10 units wide and centered on the horizontal axis values, have heights as follows: 110, 4; 120, 0; 130, 0; 140, 3; 150, 1; 160, 0; 170, 5. 110 120 130 140 150 160 170 0 2 4 6

The data listed below represent the yield for regular corn seed. Using Excel, find the 5-number summary and construct a boxplot for the following data set : 2050 1914 1306 2497 1504 1968 1435 1928 1631 2104 1897

1306, 1567.5, 1914, 2009, 2497

For the following data set, find the "5-Number Summary" that would be used in a Box-Plot (using Excel). 28 34 51 33 26 24 39 47 43 25

24, 26.5, 33.5, 42, 51

For the following data set, find the 37th Percentile (using Excel). 28 34 51 33 26 24 39 47 43 25

29.65

For the following data set, find the 2nd Quartile (using Excel). 28 34 51 33 26 24 39 47 43 25

33.5

Below are 24 sorted ages of an acting award winner. Find the 82nd Percentile using Excel. 30 31 32 32 36 40 41 47 47 49 52 53 54 55 56 59 61 62 64 64 68 71 78 80

Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

70-105 =.6065

Assume that adults have IQ scores that are normally distributed with a mean of 100100 and a standard deviation 2020. Find Upper P 9P9, which is the IQ score separating the bottom 99% from the top 9191%.

73.2

About _____% of the area is between zequals=negative 2−2 and zequals=22 (or within 22 standard deviationsdeviations of the mean).

95.44

Heights of men on a baseball team have a bell-shaped distribution with a mean of 170 cm170 cm and a standard deviation of 6 cm6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 152152 cm and 188188 cm b. 164164 cm and 176176 cm

99.7% of the men are between 152152 cm and 188188 cm. 68% of the men are between 164164 cm and 176176 cm.

A scatterplot is a plot of paired data (x,y) and is helpful in determining whether there is a relationship between the two variables.

A scatterplot (or scatter diagram) is a plot of paired (x,y) quantitative data with a horizontal x-axis and a vertical y-axis. The horizontal axis is used for the first (x) variable, and the vertical axis is used for the second variable. The pattern of the plotted points is often helpful in determining whether there is a relationship between the two variables.

A histogram aids in analyzing the _______ of the data.

A shape of the distribution. A histogram is a visual tool used to represent and analyze data. It is basically a graphic version of a frequency distribution, and it can show the center, variation, and the shape of the distribution of the data.

What is a self-interest study?

A survey in which the sponsor can enjoy monetary or other gains from the results A self-interest study is a survey in which the sponsor can enjoy monetary or other gains from the results. Be very wary of studies where the sponsor has certain interests to promote.

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The time it takes for a light bulb to burn outtime it takes for a light bulb to burn out b. The number of points scored during a basketball gamenumber of points scored during a basketball game c. The gender of college studentsgender of college students d. The number of fish caught during a fishing tournamentnumber of fish caught during a fishing tournament e. The number of textbook authors now sitting at a computernumber of textbook authors now sitting at a computer f. The time required to download a file from the Internet

A- Contin B - Discrete C - not random D - Discrete E - Discrete F - Continuous

What requirements are necessary for a normal probability distribution to be a standard normal probability distribution? Choose the correct answer below.

A. The mean and standard deviation have the values of mu equals 0μ=0 and sigma equals 1.

A multiple choice test has 7 questions, each with 4 answers. Find the probability of 4 correct answers and 3 wrong answers.

A. left parenthesis one fourth right parenthesis Superscript 4 Baseline left parenthesis three fourths right parenthesis cubed 1 44 3 43

View an Example Question Help To the right are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event. a. Among three children, there areare exactly 22 girlsgirls. b. Among three children, there areare exactly 22 boysboys. c. Among three children, there areare exactly 33 girlsgirls.

Assume that a given procedure has n different simple events and that each of those simple events has an equal chance of occurring. If event A can occur in s of these n ways, then Upper P left parenthesis Upper A right parenthesis equals StartFraction number of ways Upper A can occur Over number of different simple events EndFraction equals StartFraction s Over n EndFractionP(A)= number of ways A can occur number of different simple events= s n The 8 simple events are listed in the table. a. Out of the 8 equally likely simple events, 3 result in exactly 22 girlsgirls, so the probability is 3/8. b. Out of the 8 equally likely simple events, 3 result in exactly 22 boysboys, so the probability is 3/8. c. Out of the 8 equally likely simple events, 1 results in exactly 33 girlsgirls, so the probability is 1/8.

Heights of women have a bell-shaped distribution with a mean of 160160 cm and a standard deviation of 77 cm. Using Chebyshev's theorem, what do we know about the percentage of women with heights that are within 22 standard deviations of the mean? What are the minimum and maximum heights that are within 22 standard deviations of the mean?

At least 7575% of women have heights within 22 standard deviations of 160160 cm. The minimum height that is within 22 standard deviations of the mean is 146146 cm. The maximum height that is within 22 standard deviations of the mean is 174174 cm.

Which of the following is not true?

A z-score is an area under the normal curve. This is the correct answer.C.

Which of the following is NOT a measure of center?

Census

The _______ tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

Central Limit Theorem

The _______ tells us that for a population with any distribution, the distribution of the sample means approaches a normal distribution as the sample size increases.

Central limit Theorem

Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their inflight serviceinflight service, Continental AirlinesContinental Airlines randomly selects 150150 flightsflights during a certain week and surveys all passengers on the flightspassengers on the flights.

Cluster

Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their inflight serviceinflight service, Continental AirlinesContinental Airlines randomly selects 4040 flightsflights during a certain week and surveys all passengers on the flightspassengers on the flights. Which type of sampling is used?

Cluster

Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their pricingpricing, Home DepotHome Depot randomly selects 7070 check out linescheck out lines during a certain week and surveys all customers in the check out linescustomers in the check out lines. Which type of sampling is used?

Cluster

Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their safety featuressafety features, Daimler minus ChryslerDaimler−Chrysler randomly selects 7070 service centersservice centers during a certain week and surveys all customers visiting the service centerscustomers visiting the service centers.

Cluster

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A manman experienced a tax audit. The tax department claimed that the manman was audited because everyoneeveryone inin fourfour randomlyrandomly selectedselected districtsdistricts waswas beingbeing audited.audited. nothing nothing nothing Which type of sampling did the tax department use?

Cluster Sampling

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A womanwoman experienced a tax audit. The tax department claimed that the womanwoman was audited because everyoneeveryone inin threethree randomlyrandomly selectedselected districtsdistricts waswas beingbeing audited.audited. nothing nothing nothing Which type of sampling did the tax department use?

Cluster sampling

Which sampling method divides the population up into sections, randomly selects some of those sections, then chooses all the members from the selected sections to study? Choose the correct answer below.

Cluster sampling involves subdividing the population and using all members from a randomly selected group of subdivisions.

Determine whether the given value is from a discrete or continuous data set. When a trucktruck is randomly selected, it is found to have a gas tank that can hold 18 gala gas tank that can hold 18 gal. Choose the correct answer below.

It is from a continuouscontinuous data set because the number of possible values is infiniteinfinite andand not countablenot countable.

Determine whether the value given below is from a discrete or continuous data set. In a test of a method of gender selection comma 730 couples used the XSORT methodIn a test of a method of gender selection, 730 couples used the XSORT method andand 407407 ofof themthem hadhad babybaby girls.girls. Choose the correct answer below.

DiscreteA discretediscrete data set because there are a finite number of possible valuesthere are a finite number of possible values nothing Your answer is correct.B.

Determine whether the given value is from a discrete or continuous data set. When a trucktruck is randomly selected, it is found to have a gas tank that can hold 19.4 gala gas tank that can hold 19.4 gal.

It is from a continuouscontinuous data set because the number of possible values is infiniteinfinite andand not countablenot countable.

If A denotes some event, what does Upper A overbarA denote? If P(A)equals=0.9960.996, what is the value of P(Upper A overbarA)? If P(A)equals=0.9960.996, is Upper A overbarA unlikely?

Event Upper A overbarA denotes the complement of event A, meaning that Upper A overbarA consists of all outcomes in which event A does not occur.

Determine whether the description corresponds to an observational study or an experiment. Thirty university students are divided into two groups. One group receives freeThirty university students are divided into two groups. One group receives free tutoring in mathematics comma the other doesn't.tutoring in mathematics, the other doesn't. After one semester comma scores on finalAfter one semester, scores on final mathematical examinations are compared.mathematical examinations are compared. Does the description correspond to an observational study or an experiment?

Experiment

Determine whether the given value is from a discrete or continuous data set. When a busbus is randomly selected, it is found to have 2 wipers2 wipers. Choose the correct answer below.

It is from a discretediscrete data set because the number of possible values is finitefinite oror countablecountable.

The capacity of an elevator is 1010 people or 15701570 pounds. The capacity will be exceeded if 1010 people have weights with a mean greater than 1570 divided by 10 equals 157 pounds.1570/10=157 pounds. Suppose the people have weights that are normally distributed with a mean of 164 lb164 lb and a standard deviation of 26 lb26 lb.

Find the probability that if a person is randomly selected, his weight will be greater than 157157 pounds. The probability is approximately 0.60610.6061. Find the probability that 1010 randomly selected people will have a mean that is greater than 157157 pounds. The probability is approximately 0.80270.8027. No, there is a good chance that 1010 randomly selected people will exceed the elevator capacity.

The capacity of an elevator is 1515 people or 23852385 pounds. The capacity will be exceeded if 1515 people have weights with a mean greater than 2385 divided by 15 equals 159 pounds.2385/15=159 pounds. Suppose the people have weights that are normally distributed with a mean of 165 lb165 lb and a standard deviation of 30 lb30 lb.

Find the probability that if a person is randomly selected, his weight will be greater than 159159 pounds. The probability is approximately 0.57930.5793. (Round to four decimal places as needed.) b. Find the probability that 1515 randomly selected people will have a mean that is greater than 159159 pounds. The probability is approximately 0.78070.7807. (Round to four decimal places as needed.) Does the elevator appear to have the correct weight limit? Why or why not? No, there is a good chance that 1515 randomly selected people will exceed the elevator capacity.

A(n) _______ distribution has a "bell" shape.

Normal. When graphed, a normal distribution has a "bell" shape. Characteristics of the bell shape are (1) the frequencies increase to a maximum, and then decrease, and (2) symmetry, with the left half of the graph roughly a mirror image of the right half. Next Question

Which of the following would be classified as categorical data?

Hair color would be classified as categorical data. Categorical data consist of names or labels that are not numbers representing counts or measurements.

Six different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (in mmHg) are listed below. Find the range, variance, and standard deviation for the given sample data. If the subject's blood pressure remains constant and the medical students correctly apply the same measurement technique, what should be the value of the standard deviation?

Ideally, the standard deviation would be zero because all the measurements should be the same.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150150 lb and 191191 lb. The new population of pilots has normally distributed weights with a mean of 157 lb157 lb and a standard deviation of 34.7 lb34.7 lb.

If a pilot is randomly selected, find the probability that his weight is between 150150 lb and 191191 lb. The probability is approximately 0.41630.4163. If 4040 different pilots are randomly selected, find the probability that their mean weight is between 150150 lb and 191191 lb. The probability is approximately 0.89900.8990. Part (a) because the seat performance for a single pilot is more important.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150150 lb and 211211 lb. The new population of pilots has normally distributed weights with a mean of 157 lb157 lb and a standard deviation of 29.2 lb29.2 lb.

If a pilot is randomly selected, find the probability that his weight is between 150150 lb and 211211 lb. The probability is approximately 0.56250.5625. (Round to four decimal places as needed.) b. If 3131 different pilots are randomly selected, find the probability that their mean weight is between 150150 lb and 211211 lb. The probability is approximately 0.90900.9090. (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? Part (a) because the seat performance for a single pilot is more important.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150150 lb and 211211 lb. The new population of pilots has normally distributed weights with a mean of 159 lb159 lb and a standard deviation of 29.8 lb29.8 lb.

If a pilot is randomly selected, find the probability that his weight is between 150150 lb and 211211 lb. The probability is approximately 0.57820.5782. b. If 4040 different pilots are randomly selected, find the probability that their mean weight is between 150150 lb and 211211 lb. The probability is approximately 0.97190.9719. c. When redesigning the ejection seat, which probability is more relevant? Part (a) because the seat performance for a single pilot is more important.

Based on a survey, for women aged 18 to 24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8114.8 and a standard deviation of 13.313.3. Complete parts (a) through (c).

If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 8080. 0.99560.9956 If 33 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 8080. 0.00050.0005 Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be used? ----Since the original population is normally distributed, the sampling distribution of sample means will be normally distributed for any sample size.

A bar chart and a Pareto chart both use bars to show frequencies of categories of categorical data. What characteristic distinguishes a Pareto chart from a bar chart, and how does that characteristic help us in understanding the data?

In a Pareto chart, the bars are always arranged in descending order according to frequencies. The Pareto chart helps us understand data by drawing attention to the more important categories, which have the highest frequencies. A bar chart uses bars of equal width to show frequencies of categorical data. The vertical scale represents frequencies or relative frequencies. The horizontal scale identifies the different categories of qualitative data. When one wants a bar chart to draw attention to the more important categories, one can use a Pareto chart, which is a bar chart for categorical data, with the added stipulation that the bars are arranged in descending order according to frequencies. The bars decrease in height from left to right.

Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their pricingpricing, AmtrakAmtrak randomly selects 4040 trainstrains during a certain week and surveys all passengers on the trainspassengers on the trains. Which type of sampling is used?

In a random sample members from the population are selected in such a way that each individual member has an equal chance of being selected. In systematic sampling, select some starting point and then select every kth element in the population. With convenience sampling, simply use results that are very easy to get. With stratified sampling, subdivide the population into at least two different subgroups (or strata) so that subjects within the same subgroup share the same characterisitcs, then draw a sample from each subgroup (or stratum). In cluster sampling, first divide the population area into sections (or clusters), then randomly select some of the clusters, and then choose all the members from those selected clusters. Cluster

Which of the following is always true?

In a symmetric and bell-shaped distribution, the mean, median, and mode are the same.

Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.

Independent

A discretediscrete data set because there are a finite number of possible valuesthere are a finite number of possible values

Interval

Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 529human resource professionals, each was asked about the importance of the appearance of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.

It appears to be sound because the data are not biased in any way.

Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 674subjects, each was asked how often he or she read a book. The survey subjects were internet users who responded to a question that was posted on a news website.

It is flawed because it is a voluntary response sample.

Determine whether the given value is from a discrete or continuous data set. When a busbus is randomly selected, it is found to have a tire pressure of 32 psia tire pressure of 32 psi. Choose the correct answer below.

It is from a continuouscontinuous data set because the number of possible values is infiniteinfinite andand not countablenot countable.

You are certainYou are certain to get 2 kings when selecting 502 kings when selecting 50 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

P=1

Which of the following is NOT a value in the 5-number summary?

Mean

Mean 1.3 SD = 1.0

In the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation. x P(x) 0 0.030.03 1 0.120.12 2 0.340.34 3 0.270.27 4 0.150.15 5 0.090.09 PrintDone

Mean 2.7 SD = 1.2

Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. x 0 1 2 3 4 5 P(x) 0.01650.0165 0.10490.1049 0.26710.2671 0.34000.3400 0.21640.2164 0.0551

Mean 2.8 SD 1.1

Groups of people aged 15-65 are randomly selected and arranged in groups of six. In the accompanying table, the random variable x is the number in the group who say that their family and/or partner contribute most to their happiness (based on a survey). x P(x) 0 0+ 1 0.0190.019 2 0.0110.011 3 0.1460.146 4 0.2870.287 5 0.3510.351 6 0.1860.186

Mean 4.5 SD 1.1

There is a 0.00780.0078 probability that a best-of-seven contest will last four games, a 0.23150.2315 probability that it will last five games, a 0.23790.2379 probability that it will last six games, and a 0.52280.5228 probability that it will last seven games. Verify that this is a probability distribution. Find its mean and standard deviation.

Mean 6.38 SD = .84

Several psychology students are unprepared for a surprise true/false test with 1616 questions, and all of their answers are guesses. a. Find the mean and standard deviation for the number of correct answers for such students. b. Would it be unusual for a student to pass by guessing (which requires getting at least 1313 correct answers)? Why or why not?

Mean 8 SD = 2 Yes because 13 is greater than the maximum usual value

Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.210.21 1 0.280.28 2 0.020.02 3 0.280.28 4 0.210.21

Yes because the probabilities sum to 1 and are all between 0 and 1 inclusive

Let the random variable x represent the number of girls in a family with three children. Assume the probability of a child being a girl is 0.350.35. The table on the right describes the probability of having x number of girls. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. Is it unusual for a family of three children to consist of three girls? x P(x) 0 0.2750.275 1 0.4440.444 2 0.2390.239 3 0.042

Mean = 1.05 SD = .83 Yes because the probability of having 3 girls is less than or equal to 0.05

In the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation. x P(x) 0 0.020.02 1 0.110.11 2 0.240.24 3 0.340.34 4 0.160.16 5 0.13

Mean = 2.7 SD = 1.2

n the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation. x P(x) 0 0.040.04 1 0.080.08 2 0.340.34 3 0.350.35 4 0.110.11 5 0.080.08

Mean = 2.7 SD = 1.2

In the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation. x P(x) 0 0.050.05 1 0.090.09 2 0.270.27 3 0.340.34 4 0.150.15 5 0.100.10

Mean = 2.8 SD 1.3

A candy company claims that 1010% of its plain candies are orange, and a sample of 200200 such candies is randomly selected. Find the mean and standard deviation for the number of orange candies in such groups of 200200.

Mean = 20 SD = 4.2

A candy company claims that 1414% of its plain candies are orange, and a sample of 200200 such candies is randomly selected.

Mean = 28 SD = 4.9

Several psychology students are unprepared for a surprise true/false test with 99 questions, and all of their answers are guesses. a. Find the mean and standard deviation for the number of correct answers for such students. b. Would it be unusual for a student to pass by guessing (which requires getting at least 77 correct answers)? Why or why not?

Mean = 4.5 SD = 1.5 No because 7 is within the range of usual values

Several psychology students are unprepared for a surprise true/false test with 1010 questions, and all of their answers are guesses. a. Find the mean and standard deviation for the number of correct answers for such students. b. Would it be unusual for a student to pass by guessing (which requires getting at least 77 correct answers)? Why or why not?

Mean = 5 SD = 1.6 no because 7 is within the range of usual values

There is a 0.12480.1248 probability that a best-of-seven contest will last four games, a 0.13460.1346 probability that it will last five games, a 0.19080.1908 probability that it will last six games, and a 0.54980.5498 probability that it will last seven games. Verify that this is a probability distribution. Find its mean and standard deviation.

Mean = 6.17 SD = 1.08

Assume that a procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean muμ and standard deviation sigmaσ. Also, use the range rule of thumb to find the minimum usual value mu minus 2 sigmaμ−2σ and the maximum usual value mu plus 2 sigmaμ+2σ. nequals=14601460, pequals=1 divided by 5

Muequals= 292292 sigmaσequals= 15.315.3 (Round to one decimal place as needed.) mu minus 2 sigmaμ−2σequals= 261.4261.4 (Round to one decimal place as needed.) mu plus 2 sigmaμ+2σequals= 322.6322.6 (Round to one decimal place as needed.)

Do one of the following, as appropriate. (a) Find the critical value z Subscript alpha divided by 2zα/2, (b) find the critical value t Subscript alpha divided by 2tα/2, (c) state that neither the normal nor the t distribution applies. Confidence level 9595%; nequals=1919; sigma is knownσ is known; population appears to be very skewedvery skewed.

Neither

Do one of the following, as appropriate. (a) Find the critical value z Subscript alpha divided by 2zα/2, (b) find the critical value t Subscript alpha divided by 2tα/2, (c) state that neither the normal nor the t distribution applies. Confidence level 9999%; nequals=2424; sigma is knownσ is known; population appears to be very skewedvery skewed.

Neither

Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.250.25 1 0.300.30 2 negative 0.10−0.10 3 0.300.30 4

No Because some of the prob have values greater than 1 and or less than 0

Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Randomly selecting 50 citizens of a state and recording their nationalitiesRandomly selecting 50 citizens of a state and recording their nationalities nothing

No Because there are more than two possible outcomes

Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.250.25 1 0.300.30 2 negative 0.10−0.10 3 0.300.30 4 0.25

No because some of the prob have values greater than 1 or less than 0

Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.250.25 1 0.300.30 2 negative 0.10−0.10 3 0.300.30 4

No because some of the probabilities have values greater than 1 or less than 0

Listed below are head injury measurements from small cars that were tested in crashes. The measurements are in "hic," which is a measurement of a standard "head injury criterion," (lower "hic" values correspond to safer cars). The listed values correspond to cars A, B, C, D, E, F, and G, respectively. Find the a. mean, b. median, c. midrange, and d. mode for the data. Also complete parts e. and f. Based on these limited results, do small cars appear to have about the same risk of head injury in a crash?

No, because the data values differ substantially.

Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general?

No, because the sample is not representative of the whole population.

Based on a study of agesages of men and women whowho have childrenhave children, a researcher concludes that being a parentbeing a parent causes people to ageage. Do you agree with this conclusion?

No. There may be a relationship between having childrenhaving children and the age of an adultthe age of an adult, but that does not mean that one causes the other.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Favorite colorsFavorite colors Choose the correct level of measurement.

Nominal

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Hair colorsHair colors Choose the correct level of measurement.

Nominal

Listed below are the annual tuition amounts of the 10 most expensive colleges in a country for a recent year. What does this "Top 10" list tell us about the population of all of that country's college tuitions? What does this "Top 10" list tell us about the population of all the country's college tuitions?

Nothing meaningful can be concluded from this information except that these are the largest tuitions of colleges in the country for a recent year.

ORDINAL

A study is conducted to measure children's growth rates without any treatment applied to the children. What best classifies this study? Choose the correct answer below.

Observational study involves observing and measuring specific characteristics without attempting to modify the subjects being studied.

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 1 equals smooth dash yellow1=smooth-yellow, 2 equals smooth dash green2=smooth-green, 3 equals wrinkled dash yellow3=wrinkled-yellow, and 4 equals wrinkled dash green4=wrinkled-green. Do the results make sense?

Only the mode makes sense since the data is nominal. Your answer is correct.B.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. The rankings of songs in the top 100The rankings of songs in the top 100 Choose the correct level of measurement.

Ordinal

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 7777 people in the 18-21 age bracket and finds that 5757 of them respond and 2020 refuse to respond. When 258258 people in the 22-29 age bracket are contacted, 235235 respond and 2323 refuse to respond. Suppose that one of the 335335 people is randomly selected. Find the probability of getting someone in the 18 dash 2118-21 age bracket or someone who respondedresponded.

P(person is in the 18 dash 2118-21 age bracket or respondedresponded)equals= 0.931

The following data lists the number of correct and wrong dosage amounts calculated by 2727 physicians. In a research experiment, a group of 1313 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 1414 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution." If one of the physicians is randomly selected, find the probability of getting one who made a correct dosage calculation or was given the bottle with a concentration label. Correct Dosage Calculation Wrong Dosage Calculation Concentration Label ("1 milligram in 1 milliliter solution") 1111 22 Ratio Label ("1 milliliter of a 1:1000 solution") 33 1111

P(physician made a correct dosage calculation or was given the bottle with a concentration label) equals= . 593.593 (Type an integer or decimal rounded to three decimal places as needed.)

In a certain study comma the chance of encountering a car crash on the roadstudy, the chance of encountering a car crash on the road is stated as 2020%. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive

P= .2

FourteenFourteen of the 100100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective?

P= .86

It is impossibleIt is impossible to get 5 aces when selecting5 aces when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

P=0

dentify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at MicrosoftMicrosoft selects every 1818th software CDsoftware CD that comes off the assembly line starting with the sixthsixth until she obtains a sample of 120120 software CDssoftware CDs.

Systematic

dentify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at ToshibaToshiba selects every 1313th laptoplaptop that comes off the assembly line starting with the thirdthird until she obtains a sample of 130130 laptopslaptops. Which type of sampling is used?

Systematic

Determine whether the distribution is a discrete probability distribution.

Yes because the probability sum to 1 and are all between 0 and 1, inclusive

A _______ histogram has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies.

Relative frequency. A histogram is a graph consisting of bars of equal width drawn adjacent to each other (without gaps). A relative frequency histogram has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies (as percentages or proportions) instead of actual frequencies. Next Question

Determine whether the results below appear to have statistical significance, and also determine whether the results have practical significance. In a study of a weight loss program, 4 subjects lost an average of 44 lbs. It is found that there is about a 21% chance of getting such results with a diet that has no effect. Does the weight loss program have statistical significance? Does the weight loss program have practical significance?

Results are said to be statistically significant if they are unlikely to occur solely by chance. No, the program is not statistically significant because the results are likely to occur by chance. The statistical significance of a study can differ from its practical significance. It is possible that, based on the available sample data, statistical methods can be used to reach a conclusion that a weight loss program is effective, but common sense might suggest that the program does not make enough of a difference to justify its use or to be practical. Yes, the program is practically significant because the amount of lost weight is large enough to be considered practically significant.

The standard deviation of the distribution of sample means is _______.

SD/sqrt of N

The _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.

Sample Space

For the binomial distribution, which formula finds the standard deviation?

Sort of npq

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A manman experienced a tax audit. The tax department claimed that the manman was audited because hehe waswas randomlyrandomly selectedselected fromfrom allall menmen inin hishis ageage group.group. nothing Which type of sampling did the tax department use?

Stratified sampling

Which sampling method subdivides the population into categories sharing similar characteristics and then selects a sample from each subdivision?

Stratified sampling method involves subdividing the population and uses a sample of members from each subdivision of the population. Next Question

Identify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General ElectricGeneral Electric selects every 1919th refrigeratorrefrigerator that comes off the assembly line starting with the tenthtenth until she obtains a sample of 8080 refrigeratorsrefrigerators. Which type of sampling is used?

Systematic

Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A manman is selected by a marketing company to participate in a paid focus group. The company says that the manman was selected because everyevery 5000 th5000th personperson inin thethe phonephone numbernumber listingslistings waswas beingbeing selected.selected. Which type of sampling did the marketing company use?

SystematicSystematic sampling

Identify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at MicrosoftMicrosoft selects every 2020th software CDsoftware CD that comes off the assembly line starting with the eightheighth until she obtains a sample of 120120 software CDssoftware CDs.

Systemic

dentify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at IBMIBM selects every 1313th computercomputer that comes off the assembly line starting with the secondsecond until she obtains a sample of 110110 computerscomputers.

Systemic

Assume that adults have IQ scores that are normally distributed with a mean of 105105 and a standard deviation 2020. Find Upper P 4P4, which is the IQ score separating the bottom 44% from the top 9696%.

The IQ score that separates the bottom 44% from the top 9696% is Upper P 4P4equals= 69.9969.99.

Assume that adults have IQ scores that are normally distributed with a mean of 105105 and a standard deviation 1515. Find Upper P 4P4, which is the IQ score separating the bottom 44% from the top 9696%.

The IQ score that separates the bottom 44% from the top 9696% is Upper P 4P4equals= 78.7478.74.

The IQ score that separates the bottom 44% from the top 9696% is Upper P 4P4equals= 78.7478.74. (Round to the nearest hundredth as needed.)

As a procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as _______.

The Law of large numbers

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z = 0.18

The area of the shaded region is . 5714.5714.

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z= .88

The area of the shaded region is . 8106.8106.

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

The area of the shaded region is 0.67360.6736.

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

The area of the shaded region is 0.74540.7454.

Using the simple random sample of weights of women from a data set, we obtain these sample statistics: nequals=3535 and x overbarxequals=148.07148.07 lb. Research from other sources suggests that the population of weights of women has a standard deviation given by sigmaσequals=31.3631.36 lb. a. Find the best point estimate of the mean weight of all women. b. Find a 9090% confidence interval estimate of the mean weight of all women.

The best point estimate is 148.07148.07 lb. (Type an integer or a decimal.) b. The 9090% confidence interval estimate is 139.35139.35 lbless than<muμless than< 156.79156.79 lb. (Round to two decimal places as needed.)

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. Assume 3.33.3% of the thermometers are rejected because they have readings that are too high and another 3.33.3% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

The cutoff values are negative 1.84 comma 1.84−1.84,1.84 degrees.

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. Assume 3.23.2% of the thermometers are rejected because they have readings that are too high and another 3.23.2% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

The cutoff values are negative 1.85 comma 1.85−1.85,1.85 degrees.

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. Assume 2.52.5% of the thermometers are rejected because they have readings that are too high and another 2.52.5% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

The cutoff values are negative 1.96 comma 1.96−1.96,1.96 degrees.

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. Assume 2.42.4% of the thermometers are rejected because they have readings that are too high and another 2.42.4% are rejected because they have readings that are too low. Draw a sketch and find the two readings that are cutoff values separating the rejected thermometers from the others.

The cutoff values are negative 1.98 comma 1.98−1.98,1.98 degrees.

Fuel consumption is commonly measured in miles per gallon (mi/gal). An agency designed new fuel consumption tests to be used starting with 2008 car models. Listed below are randomly selected amounts by which the measured MPG ratings decreased because of the new 2008 standards. Find the range, variance, and standard deviation for the sample data. Is the decrease of 4 mi/gal unusual? Why or why not?

The decrease of 4 mi/gal is unusualunusual because it is more thanmore than two standard deviations fromfrom the mean.

An insurance institute conducted tests with crashes of new cars traveling at 6 mi/h. The total cost of the damages was found for a simple random sample of the tested cars and listed below. Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. Do the different measures of center differ very much?

The different measures of center do not differ by very large amounts.

Which of the following is NOT a conclusion of the Central Limit Theorem?

The distribution of the sample data will approach a normal distribution as the sample size increases.

Which of the following is NOT a conclusion of the Central Limit Theorem? Choose the correct answer below.

The distribution of the sample data will approach a normal distribution as the sample size increases.

Which is relatively better: a score of 5050 on a psychology test or a score of 5959 on an economics test? Scores on the psychology test have a mean of 8585 and a standard deviation of 1212. Scores on the economics test have a mean of 6565 and a standard deviation of 44. Choose the correct answer below.

The economicseconomics test score is relatively better because its z score is greater than the z score for the psychologypsychology test score.

Which is relatively better: a score of 6363 on a psychology test or a score of 3737 on an economics test? Scores on the psychology test have a mean of 8686 and a standard deviation of 1313. Scores on the economics test have a mean of 4545 and a standard deviation of 66.

The economicseconomics test score is relatively better because its z score is greater than the z score for the psychologypsychology test score.

Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".) Randomly selecting aa carcar from the vehiclevehicle assembly line and getting one that is free of defects. Randomly selecting aa carcar from the vehiclevehicle assembly line and getting one with a dead batterydead battery. Choose the correct answer below.

The events are disjoint. They cannot occur at the same time.

Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".) Randomly selecting aa violinviolin from the instrumentinstrument assembly line and getting one that is free of defects. Randomly selecting aa violinviolin from the instrumentinstrument assembly line and getting one with a warped neckwarped neck.

The events are disjoint. They cannot occur at the same time.

Randomly selecting aa trucktruck from the vehiclevehicle assembly line and getting one that is free of defects. Randomly selecting aa trucktruck from the vehiclevehicle assembly line and getting one with a dead batterydead battery.

The events are disjoint. They cannot occur at the same time.

Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".) Receiving a phone call from a volunteer survey subject who believes that Roe versus Wade needs to be overturnedRoe versus Wade needs to be overturned. Receiving a phone call from a volunteer survey subject who is opposed to a complete spending freeze.

The events are not disjoint. They can occur at the same time.

Use the data in the following table, which summarizes results from 156156 pedestrian deaths that were caused by accidents. If two different deaths are randomly selected without replacement, find the probability that they both involved intoxicated drivers.

The formal multiplication rule is that Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis times Upper P left parenthesis B|A right parenthesisP(A and B)=P(A)•P(B|A), where P(B|A) is the probability of B occurring given that A has occurred.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Placements of swimmers in a swim meetPlacements of swimmers in a swim meet Choose the correct level of measurement.

The four levels of measurement are summarized as follows: Nominal Categories only; data cannot be arranged in an ordering scheme. Ordinal Categories are ordered, but differences cannot be found or are meaningless. Interval Differences are meaningful, but there is no natural zero starting point and ratios are meaningless. Ratio There is a natural zero starting point and ratios are meaningful. ORDINAL

Determine whether the given description corresponds to an observational study or an experiment. In a study of 381381 girlsgirls with a particular disease, the subjects were injected with vitamins towere injected with vitamins to determine if the vitamins have an effect on the disease.determine if the vitamins have an effect on the disease. Does the given description correspond to an observational study or an experiment?

The given description corresponds to an experimentan experiment.

Determine whether the given description corresponds to an observational study or an experiment. In a study of 359359 womenwomen with a particular disease, the subjects were monitored with an EEGwere monitored with an EEG while asleep.while asleep. Does the given description correspond to an observational study or an experiment?

The given description corresponds to an observational studyan observational study.

Determine whether the given description corresponds to an observational study or an experiment. In a study of 408408 womenwomen with a particular disease, the subjects were monitored with an EEGwere monitored with an EEG while asleep.

The given description corresponds to an observational studyan observational study.

Determine whether the given description corresponds to an observational study or an experiment. In a study of 443443 menmen with a particular disease, the subjects were photographed daily.were photographed daily. nothing Does the given description correspond to an observational study or an experiment?

The given description corresponds to an observational studyan observational study.

Which of the following does NOT describe the standard normal distribution?

The graph is uniform.

Listed below are the gross amounts (in millions of dollars) earned in box office receipts for a recent movie. The amounts are listed in order for the first 14 days of the movies release. Find the range, variance, and standard deviation of the data set. If you invested in this movie, what characteristic of the data set would you care about most, and is it a measure of center or variation?

The gross from opening day and the rate of decline. The measures of center and variation are less important.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Critic ratings of movies on a scale from 1 star to 7 stars.Critic ratings of movies on a scale from 1 star to 7 stars. Choose the correct answer below.

The ordinalordinal level of measurement is most appropriate because categories are ordered commacategories are ordered, but differencesbut differences cannot be found or are meaninglesscannot be found or are meaningless.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Ranks of cars evaluated by a consumer's magazine.Ranks of cars evaluated by a consumer's magazine. Choose the correct answer below.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Ratings of hotels on a scale from 0 stars to 4 stars.Ratings of hotels on a scale from 0 stars to 4 stars. Choose the correct answer below.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Ratings of hotels on a scale from 0 stars to 7 stars.Ratings of hotels on a scale from 0 stars to 7 stars. Choose the correct answer below.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Alert system of yellow left parenthesis lowest right parenthesis comma orange comma and red left parenthesis highest right parenthesis

The ordinalordinal level of measurement is most appropriate because the data can becan be ordered commaordered, butbut differences left parenthesis obtained by subtraction right parenthesisdifferences (obtained by subtraction) cannotcannot be foundbe found or areor are meaningless.meaningless. nothing nothing

Men's heights are normally distributed with mean 68.668.6 in and standard deviation of 2.8 in.2.8 in. Women's heights are normally distributed with mean 63.763.7 in and standard deviation of 2.52.5 in. The standard doorway height is 8080 in. a. What percentage of men are too tall to fit through a standard doorway without bending, and what percentage of women are too tall to fit through a standard doorway without bending? b. If a statistician designs a house so that all of the doorways have heights that are sufficient for all men except the tallest 5%, what doorway height would be used?

The percentage of men who are too tall to fit through a standard door without bending is 0.000.00%. The percentage of women who are too tall to fit through a standard door without bending is 0.000.00%. The statistician would design a house with doorway height 73.273.2 in.

Men's heights are normally distributed with mean 7070 in and standard deviation of 2.8 in.2.8 in. Women's heights are normally distributed with mean 63.763.7 in and standard deviation of 2.52.5 in. The standard doorway height is 8080 in. a. What percentage of men are too tall to fit through a standard doorway without bending, and what percentage of women are too tall to fit through a standard doorway without bending? b. If a statistician designs a house so that all of the doorways have heights that are sufficient for all men except the tallest 5%, what doorway height would be used?

The percentage of men who are too tall to fit through a standard door without bending is 0.020.02%. (Round to two decimal places as needed.) The percentage of women who are too tall to fit through a standard door without bending is 0.000.00%. (Round to two decimal places as needed.) b. The statistician would design a house with doorway height 74.674.6 in. (Round to the nearest tenth as needed.)

The probability is 0.97880.9788.

A survey found that women's heights are normally distributed with mean 63.463.4 in and standard deviation 2.52.5 in. A branch of the military 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 this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

The percentage of women who meet the height requirement is 98.4698.46%. (Round to two decimal places as needed.) Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? No, because only a small percentage of women are not allowed to join this branch of the military because of their height. For the new height requirements, this branch of the military requires women's heights to be at least 57.657.6 in and at most 68.568.5 in.

A survey found that women's heights are normally distributed with mean 63.963.9 in and standard deviation 2.32.3 in. A branch of the military 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 this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

The percentage of women who meet the height requirement is 99.4899.48%. (Round to two decimal places as needed.) Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? A. No, because only a small percentage of women are not allowed to join this branch of the military because of their height. b. For the new height requirements, this branch of the military requires women's heights to be at least 58.558.5 in and at most 68.668.6 in.

In a certain instant lottery game comma the chances of a wininstant lottery game, the chances of a win are stated as "22 in 1717." Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

The probability is . 118.118.

The probability is 0.01430.0143.

Assume the readings on thermometers are normally distributed with a mean of 0degrees°C and a standard deviation of 1.00degrees°C. Find the probability that a randomly selected thermometer reads between negative 1.79−1.79 and negative 1.07−1.07 and draw a sketch of the region.

The probability is 0.10560.1056.

Assume the readings on thermometers are normally distributed with a mean of 0degrees°C and a standard deviation of 1.00degrees°C. Find the probability that a randomly selected thermometer reads between negative 1.19−1.19 and negative 0.46−0.46 and draw a sketch of the region.

The probability is 0.20580.2058.

The probability is 0.53590.5359.

Assume that women's heights are normally distributed with a mean given by mu equals 63.4 inμ=63.4 in, and a standard deviation given by sigma equals 2.3 inσ=2.3 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 6464 in. (b) If 3636 women are randomly selected, find the probability that they have a mean height less than 6464 in.

The probability is approximately 0.60290.6029. (Round to four decimal places as needed.) (b) The probability is approximately 0.94120.9412. (Round to four decimal places as needed.)

Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why? Pre-Employment Drug Screening Results

The probability of a false positive test result is . 183.183. Who would suffer from a false positive result? Why? The person tested would suffer because he or she would be suspected of using drugs when in reality he or she does not use drugs.

What does P(B|A) represent?

The probability of event B occurring after it is assumed that event A has already occurred

The probability of getting a green pea is approximately . 964.964. no, it is notis not reasonably close.

In a test of a gender-selection technique, results consisted of 212212 baby girls and 234234 baby boys. Based on this result, what is the probability of a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?

The probability that a girl will be born using this technique is approximately . 475.475. Does the technique appear effective in improving the likelihood of having a girl baby? -no

In a test of a gender-selection technique, results consisted of 224224 baby girls and 221221 baby boys. Based on this result, what is the probability of a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl? Does the technique appear effective in improving the likelihood of having a girl baby?

The probability that a girl will be born using this technique is approximately 0.5030.503. No

n a test of a gender-selection technique, results consisted of 294294 baby girls and 1313 baby boys. Based on this result, what is the probability of a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl? Does the technique appear effective in improving the likelihood of having a girl baby?

The probability that a girl will be born using this technique is approximately 0.9580.958. (Type an integer or decimal rounded to three decimal places as needed.) Yes.

Among respondents asked which is their favorite seat on a plane, 489489 chose the window seat, 99 chose the middle seat, and 304304 chose the aisle seat. What is the probability that a passenger prefers the middle seat? Is it unlikely for a passenger to prefer the middle seat? If so, why is the middle seat so unpopular?

The probability that a passenger prefers the middle seat is . 011.011. Is it unlikely for a passenger to prefer the middle seat? Yes, because the probability that a passenger prefers the middle seat is less than 0.05. If so, why is the middle seat so unpopular? The middle seat lacks an outside view, easy access to the aisle, and a passenger in the middle seat has passengers on both sides instead of on one side only.

he lengths of pregnancies are normally distributed with a mean of 268268 days and a standard deviation of 1515 days. a. Find the probability of a pregnancy lasting 308308 days or longer. b. If the length of pregnancy is in the lowest 22%, then the baby is premature. Find the length that separates premature babies from those who are not premature.

The probability that a pregnancy will last 308308 days or longer is . 0038.0038. (Round to four decimal places as needed.) b. Babies who are born on or before 237237 days are considered premature.

The probability that a randomly selected adult has an IQ between 8585 and 115115 is 0.5467 .

The probability that a randomly selected adult has an IQ between 8686 and 114114 is 0.51610.5161.

Among 400400 randomly selected drivers in the 16 minus 1816−18 age bracket, 277277 were in a car crash in the last year. If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will be in a car crash during the next year? Is it unlikely for a driver in that age bracket to be involved in a car crash during a year? Is the resulting value high enough to be of concern to those in the 16 minus 1816−18 age bracket? Consider an event to be "unlikely" if its probability is less than or equal to 0.05.

The probability that a randomly selected person in the 16 minus 1816−18 age bracket will be in a car crash this year is approximately . 693.693. Would it be unlikely for a driver in that age bracket to be involved in a car crash this year? -no Is the probability high enough to be of concern to those in the 16 minus 1816−18 age bracket? -yes

Refer to the sample data for polygraph tests shown below. If one of the test subjects is randomly selected, what is the probability that the subject is not lying? Is the result close to the probability of 0.4210.421 for a negative test result?

The probability that a randomly selected polygraph test subject was not lying is . 463.463. Is the result close to the probability, rounded to three decimal places, of 0.4210.421 for a negative test result? Yes, because there is less than a 0.050 absolute difference between the probability of a true response and the probability of a negative test resul

peas are generated from parents having the green/yellow pair of genes, so there is a 0.750.75 probability that an individual pea will have a green pod. Find the probability that among the 1313 offspring peas, at leastat least 1212 havehave green pods.pods. Is it unusual to get at leastat least 1212 peaspeas with greengreen podspods when 1313 offspring peas are generated? Why or why not?

The probability that at leastat least 1212 of the 1313 offspring peas havehave green podspods is 0.127 Is it unusual to randomly select 1313 peas and find that at leastat least 1212 of them have a green pod? Note that a small probability is one that is less than 0.05. No, because the probability of this occurring is notis not small.

FourteenFourteen peas are generated from parents having the green/yellow pair of genes, so there is a 0.750.75 probability that an individual pea will have a green pod. Find the probability that among the 1414 offspring peas, at leastat least 1313 havehave green pods.pods. Is it unusual to get at leastat least 1313 peaspeas with greengreen podspods when 1414 offspring peas are generated? Why or why not?

The probability that at leastat least 1313 of the 1414 offspring peas havehave green podspods is 0.1010.101. (Round to three decimal places as needed.) Is it unusual to randomly select 1414 peas and find that at leastat least 1313 of them have a green pod? Note that a small probability is one that is less than 0.05. No, because the probability of this occurring is notis not small. This is the correct answer.C.

peas are generated from parents having the green/yellow pair of genes, so there is a 0.750.75 probability that an individual pea will have a green pod. Find the probability that among the 99 offspring peas, at leastat least 88 havehave green pods.pods. Is it unusual to get at leastat least 88 peaspeas with greengreen podspods when 99 offspring peas are generated? Why or why not?

The probability that at leastat least 88 of the 99 offspring peas havehave green podspods is . 3.3. (Round to three decimal places as needed.) Is it unusual to randomly select 99 peas and find that at leastat least 88 of them have a green pod? Note that a small probability is one that is less than 0.05. No because the probability of this occurring is notis not small.

A brand name has aa 4040% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 66 randomly selected consumers. Complete parts (a) through (d) below.

The probability that exactly 55 of the 66 consumers recognize the brand name is 0.0370.037. The probability that all of the selected consumers recognize the brand name is 0.0040.004. The probability that at least 55 of the selected consumers recognize the brand name is 0.0410.041. If 66 consumers are randomly selected, is 55 an unusually high number of consumers that recognize the brand name? ---Yes , because the probability that 55 or more of the selected consumers recognize the brand name is lessless than 0.05.

Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.090.09 1 0.210.21 2 0.400.40 3 0.210.21 4 0.090.09

Yes because the probabilities sum to 1 and are all between 0 and 1, inclusive

ThirteenThirteen peas are generated from parents having the green/yellow pair of genes, so there is a 0.750.75 probability that an individual pea will have a green pod. Find the probability that among the 1313 offspring peas, no more thanno more than 11 has ahas a green pod.pod. Is it unusual to get no more thanno more than 11 peapea with a greena green podpod when 1313 offspring peas are generated? Why or why not?

The probability that no more thanno more than 11 of the 1313 offspring peas has ahas a green podpod is 0.0000.000. (Round to three decimal places as needed.) Is it unusual to randomly select 1313 peas and find that no more thanno more than 11 of them have a green pod? Note that a small probability is one that is less than 0.05. yes because the prob of this occurring is very small

peas are generated from parents having the green/yellow pair of genes, so there is a 0.750.75 probability that an individual pea will have a green pod. Find the probability that among the 1515 offspring peas, no more thanno more than 11 has ahas a green pod.pod. Is it unusual to get no more thanno more than 11 peapea with a greena green podpod when 1515 offspring peas are generated? Why or why not?

The probability that no more thanno more than 11 of the 1515 offspring peas has ahas a green podpod is 0.0000.000. (Round to three decimal places as needed.) Is it unusual to randomly select 1515 peas and find that no more thanno more than 11 of them have a green pod? Note that a small probability is one that is less than 0.05. A. YesYes, because the probability of this occurring is veryis very small.

An airline has a policy of booking as many as 1212 persons on an airplane that can seat only 1111. (Past studies have revealed that only 86.086.0% of the booked passengers actually arrive for the flight.) Find the probability that if the airline books 1212 persons, not enough seats will be available. Is it unlikely for such an overbooking to occur?

The probability that not enough seats will be available is . 1637.1637. (Round to four decimal places as needed.) Is it unlikely for such an overbooking to occur? A. It is notis not unlikely for such an overbooking to occur, because the probability of the overbooking is greatergreater than 0.05.

An airline has a policy of booking as many as 1717 persons on an airplane that can seat only 1616. (Past studies have revealed that only 82.082.0% of the booked passengers actually arrive for the flight.) Find the probability that if the airline books 1717 persons, not enough seats will be available. Is it unlikely for such an overbooking to occur?

The probability that not enough seats will be available is 0.03430.0343. It isis unlikely for such an overbooking to occur, because the probability of the overbooking is less than or equal toless than or equal to than 0.05. This is the correct answer.B.

An airline has a policy of booking as many as 1717 persons on an airplane that can seat only 1616. (Past studies have revealed that only 87.087.0% of the booked passengers actually arrive for the flight.) Find the probability that if the airline books 1717 persons, not enough seats will be available. Is it unlikely for such an overbooking to occur?

The probability that not enough seats will be available is 0.09370.0937. It is notis not unlikely for such an overbooking to occur, because the probability of the overbooking is greatergreater than 0.05.

An airline has a policy of booking as many as 1515 persons on an airplane that can seat only 1414. (Past studies have revealed that only 86.086.0% of the booked passengers actually arrive for the flight.) Find the probability that if the airline books 1515 persons, not enough seats will be available. Is it unlikely for such an overbooking to occur?

The probability that not enough seats will be available is 0.10410.1041. Is it unlikely for such an overbooking to occur? It is notis not unlikely for such an overbooking to occur, because the probability of the overbooking is greatergreater than 0.05.

An airline has a policy of booking as many as 1010 persons on an airplane that can seat only 99. (Past studies have revealed that only 85.085.0% of the booked passengers actually arrive for the flight.) Find the probability that if the airline books 1010 persons, not enough seats will be available. Is it unlikely for such an overbooking to occur?

The probability that not enough seats will be available is 0.19690.1969. (Round to four decimal places as needed.) Is it unlikely for such an overbooking to occur? It is notis not unlikely for such an overbooking to occur, because the probability of the overbooking is greatergreater than 0.05.

A research center poll showed that 8181% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . 19.19.

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 1010 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 22% rate of defects, what is the probability that this whole shipment will be accepted?

The probability that this whole shipment will be accepted is . 984.984.

A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 1313 tablets. The entire shipment is accepted if at most 2 tablets do not meet the required specifications. If a particular shipment of thousands of aspirin tablets actually has a 3.03.0% rate of defects, what is the probability that this whole shipment will be accepted?

The probability that this whole shipment will be accepted is . 994.994.

Which is relatively better: a score of 8888 on a psychology test or a score of 2828 on an economics test? Scores on the psychology test have a mean of 9595 and a standard deviation of 1414. Scores on the economics test have a mean of 5252 and a standard deviation of 99. Choose the correct answer below.

The psychologypsychology test score is relatively better because its z score is greater than the z score for the economicseconomics test score.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Brain volumes measured in cubic cmBrain volumes measured in cubic cm Choose the correct answer below.

The ratioratio level of measurement is most appropriate because the data can becan be ordered commaordered, differencesdifferences can becan be foundfound and areand are meaningful commameaningful, and thereand there is ais a naturalnatural startingstarting zerozero point.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Car lengths measured in feet

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Car lengths measured in feetCar lengths measured in feet Choose the correct answer below.

A particular country has 4040 total states. If the areas of allof all 4040 states are added and the sum is divided by 4040, the result is 207 comma 699207,699 square kilometers. Determine whether this result is a statistic or a parameter. Choose the correct answer below.

The result is a parameterparameter because it describes some characteristic of a populationpopulation

A particular country has 4545 total states. If the areas of allof all 4545 states are added and the sum is divided by 4545, the result is 202 comma 196202,196 square kilometers. Determine whether this result is a statistic or a parameter.

The result is a parameterparameter because it describes some characteristic of a populationpopulation.

A particular country has 5555 total states. If the areas of allof all 5555 states are added and the sum is divided by 5555, the result is 212 comma 072212,072 square kilometers. Determine whether this result is a statistic or a parameter. Choose the correct answer below. A.

The result is a parameterparameter because it describes some characteristic of a populationpopulation. This is the correct answer.B.

A particular country has 4040 total states. If the areas ofof 2525 states are added and the sum is divided by 2525, the result is 204 comma 608204,608 square kilometers. Determine whether this result is a statistic or a parameter. Choose the correct answer below.

The result is a statisticstatistic because it describes some characteristic of a samplesample.

A particular country has 6060 total states. If the areas ofof 2020 states are added and the sum is divided by 2020, the result is 179 comma 532179,532 square kilometers. Determine whether this result is a statistic or a parameter. Choose the correct answer below.

The result is a statisticstatistic because it describes some characteristic of a samplesample.

What is the standard error of the mean?

The standard deviation of the sample means.

Determine whether the description below corresponds to an observational study or an experiment. In a studystudy sponsored by a company, 14 comma 66914,669 people were asked what contributes most to their sadness commasadness, and 36 %36% of the respondents said that it was their partner.partner. Is the study described above an observational study or an experiment?

The study is an observational study because the survey subjects were not given any treatment.

Identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance.

The symbol for sample standard deviation is s The symbol for population standard deviation is σ The symbol for sample variance is s squared The symbol for population variance is sigma squared .

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 92P92, the 92 nd92nd percentile. This is the temperature reading separating the bottom 92 %92% from the top 8 %.

The temperature for Upper P 92P92 is approximately 1.411.41degrees°.

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 93P93, the 93 rd93rd percentile. This is the temperature reading separating the bottom 93 %93% from the top 7 %.

The temperature for Upper P 93P93 is approximately 1.481.48degrees°.

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 95P95, the 95 th95th percentile. This is the temperature reading separating the bottom 95 %95% from the top 5 %.

The temperature for Upper P 95P95 is approximately 1.641.64degrees°.

Assume that adults have IQ scores that are normally distributed with a mean of 100100 and a standard deviation of 15. Find the third quartile Upper Q 3Q3, which is the IQ score separating the top 25% from the others.

The third quartile, Upper Q 3Q3, is 110.1

Assume that adults have IQ scores that are normally distributed with a mean of 101101 and a standard deviation of 15. Find the third quartile Upper Q 3Q3, which is the IQ score separating the top 25% from the others.

The third quartile, Upper Q 3Q3, is 111.1

Assume that adults have IQ scores that are normally distributed with a mean of 106106 and a standard deviation of 15. Find the third quartile Upper Q 3Q3, which is the IQ score separating the top 25% from the others.

The third quartile, Upper Q 3Q3, is 116.1116.1.

Assume that adults have IQ scores that are normally distributed with a mean of 107107 and a standard deviation of 15. Find the third quartile Upper Q 3Q3, which is the IQ score separating the top 25% from the others.

The third quartile, Upper Q 3Q3, is 117.1

Waiting times (in minutes) of customers in a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the mean and median for each of the two samples, then compare the two sets of results.

The times for customers in individual lines are much more varied than the times for customers in a single line.

Which of the following is not a requirement of the binomial probability distribution?

The trials must be dependent.

Which of the following is not a requirement of the binomial probability distribution? Choose the correct answer below.

The trials must be dependent.

In a clinical trial of a cholesterol drug, 417417 subjects were given a placebo, and 1414% of them developed headaches. For such randomly selected groups of 417417 subjects given a placebo, identify the values of n, p, and q that would be used for finding the mean and standard deviation for the number of subjects who develop headaches.

The value of n is 417417. The value of p is . 14.14. (Type an integer or a decimal.) The value of q is . 86.86.

Assume that the given procedure yields a binomial distribution with n trials and the probability of success for one trial is p. Use the given values of n and p to find the mean muμ and standard deviation sigmaσ. Also, use the range rule of thumb to find the minimum usual value mu minus 2 sigmaμ−2σ and the maximum usual value mu plus 2 sigmaμ+2σ. In an analysis of preliminary test results from a gender-selection method, 3737 babies are born and it is assumed that 50% of babies are girls, so nequals=3737 and pequals=0.50.5.

The value of the mean is muμequals= 18.518.5. (Simplify your answer.) The value of the standard deviation is sigmaσequals= 33. (Round to one decimal place as needed.) The minimum usual value is mu minus 2 sigmaμ−2σequals= 12.512.5. (Round to one decimal place as needed.) The maximum usual value is mu plus 2 sigmaμ+2σequals= 24.524.5. (Round to one decimal place as needed.)

When fourteen different second-year medical students measured the blood pressure of the same person, they obtained the results listed below. Assuming that the population standard deviation is known to be 1515 mmHg, construct and interpret a 9090% confidence interval estimate of the population mean. 139139 134134 145145 135135 131131 125125 121121 146146 121121 145145 139139 122122 128128 150150

What is the 9090% confidence interval for the population mean muμ? 127.8127.8less than<muμless than< 141.0141.0

A particular group of men have heights with a mean of 180180 cm and a standard deviation of 77 cm. CarlCarl had a height of 200200 cm. a Convert CarlCarl's height to a z score. b If we consider "usual" heights to be those that convert to z scores between minus−2 and 2, is CarlCarl's height usual or unusual?

The z score is 2.862.86. Unusual

With a height of 6969 in, MarvinMarvin was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 72.372.3 in and a standard deviation of 1.21.2 in. a. Convert MarvinMarvin's height to a z score. b. If we consider "usual" heights to be those that convert to z scores between minus−2 and 2, is MarvinMarvin's height usual or unusual?

The z score is negative 2.75−2.75. Unusual

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus−2.00, minus−1.00, 0, 1.00, 2.00? Why?

The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores

Determine whether the source given below has the potential to create a bias in a statistical study. A certain medical organization tends to oppose the use of meat and dairy products in our diets, and that organization has received hundreds of thousands of dollars in funding from an animal rights foundation.

There does appear to be a potential to create a bias. There is an incentive to produce results that are in line with the organization's creed and that of its funders. In this case, there is a potential to create a bias because the medical organization could have an incentive to produce results favorable to its funder, the animal rights foundation. One should be very wary of a study in which the sponsor can somehow profit from the results because there is an incentive to produce biased results.

Listed below are the lead concentrations (in mg/g) measured in different samples of a medicine. What do the results suggest about the safety of this medicine? What do the decimal values of the listed amounts suggest about the precision of the measurements?

There is not enough information for any meaningful conclusion. They are rounded to one half unit measurements.

What is the goal of learning statistics?

To learn to distinguish between statistical conclusions that are likely to be valid and those that are seriously flawed Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data. Statisticians universally agree that statistical thinking is good, but there are different views of what actually constitutes statistical thinking. Statistical thinking involves critical thinking and the ability to make sense of results. Statistical thinking might involve determining whether results are statistically significant.

If values are converted to standard z-scores, then procedures for working with all normal distributions are the same as those for the standard normal distribution.

True

The area in any normal distribution bounded by some score x is the same as the area bounded by the equivalent z-score in the standard normal distribution.

True

A data value is considered _______ if its z-score is less than minus−2 or greater than 2.

Unusual

In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)equals=0.7300.730, where D is directly in person. If someone is randomly selected, what does Upper P left parenthesis Upper D overbar right parenthesisPD represent, and what is its value?

Upper P left parenthesis Upper D overbar right parenthesisPD is the probability of randomly selecting someone who does not choose a direct in-person encounter as the most fun way to flirt. Upper P left parenthesis Upper D overbar right parenthesisPDequals= . 27.27 (Simplify your answer.)

In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)equals=0.6300.630, where D is directly in person. If someone is randomly selected, what does Upper P left parenthesis Upper D overbar right parenthesisPD represent, and what is its value?

Which of the following is NOT one of the three methods for finding binomial probabilities that is found in the chapter on discrete probability distributions?

Use simulation

In a random study of 420 comma 062420,062 people surveyed it was found that 138138 of them recognized a Name Brand.

Use the sample data to construct a 9595% confidence interval estimate of the percentage of people who recognize this Name Brand. 0.02740.0274%less than<pless than< 0.03830.0383%

Which of the following is NOT a misuse of statistics?

Utilizing valid statistical methods and correct sampling techniques Whether conducting a statistical analysis of data that we have collected, or analyzing a statistical analysis done by someone else, we should not rely on blind acceptance of mathematical calculations. We should consider the factors below. bullet• Context of the data bullet• Source of the data bullet• Sampling method bullet• Conclusions bullet• Practical implications When doing so, it is important to utilize valid statistical methods and correct sampling techniques. Next Question

Fill in the blank. The square of the standard deviation is called the _______.

Variance

The square of the standard deviation is called the _______.

Variance

Randomly selected students participated in an experiment to test their ability to determine when one minute (or sixty seconds) has passed. Forty students yielded a sample mean of 59.559.5 seconds. Assuming that sigmaσequals=10.610.6 seconds, construct and interpret a 9999% confidence interval estimate of the population mean of all students.

What is the 9999% confidence interval for the population mean muμ? 55.255.2less than<muμless than< 63.863.8

A random sample of the height of 25 children has a mean of 47.5 inches and a standard deviation of 2.1. Construct a 95% confidence interval estimate of the mean height for all children. Assume the population is normally distributed.

What is the confidence interval estimate of the mean height for all children? 46.6346.63inchesless than<muμless than< 48.3748.37inches

Determine whether the distribution is a discrete probability distribution.

Yes because the prob sum to 1 and are all between 0 and 1, inclusive

Listed below are measured amounts of lead (in micrograms per cubic meter, or mu g divided by m cubedμg/m3) in the air. The EPA has established an air quality standard for lead of 1.5 mu g divided by m cubedμg/m3. The measurements shown below were recorded at a building on different days. Use the given values to construct a 9595% confidence interval estimate of the mean amount of lead in the air. Is there anything about this data set suggesting that the confidence interval might not be very good? 5.405.40 0.900.90 0.450.45 0.760.76 0.850.85 1.201.20

What is the confidence interval for the population mean muμ? negative 0.380−0.380 mu g divided by m cubedμg/m3less than<muμless than< 3.5663.566 mu g divided by m cubedμg/m3

he principle of redundancy is used when system reliability is improved through redundant or backup components. A region's government requires that commercial aircraft used for flying in hazardous conditions must have two independent radios instead of one. Assume that for a typical flight, the probability of a radio failure is 0.00410.0041. What is the probability that a particular flight will be threatened with the failure of both radios? Describe how the second independent radio increases safety in this case.

What is the probability that a particular flight will be threatened with the failure of both radios? . 000017.000017 (Round to six decimal places as needed.) Describe how the second independent radio increases safety in this case. Choose the correct answer below. With one radio there is a 0.00410.0041 probability of a serious problem, but with two independent radios, the probability of a serious problem decreases substantially. The flight becomes much safer with two independent radios.

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 14.214.2% daily failure rate. Complete parts (a) through (d) below.

What is the probability that the student's alarm clock will not work on the morning of an important final exam? . 142.142 (Round to three decimal places as needed.) If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? . 02016.02016 (Round to five decimal places as needed.) What is the probability of not being awakened if the student uses three independent alarm clocks? . 00286.00286 (Round to five decimal places as needed.)

The population of ages at inauguration of all U.S. Presidents who had professions in the military is 62, 46, 68, 64, 57. Why does it not make sense to construct a histogram for this data set?

With a data set that is so small, the true nature of the distribution cannot be seen with a histogram.

The population of ages at inauguration of all U.S. Presidents who had professions in the military is 62, 46, 68, 64, 57. Why does it not make sense to construct a histogram for this data set? Choose the correct answer below.

With a data set that is so small, the true nature of the distribution cannot be seen with a histogram.

The population of ages at inauguration of all U.S. Presidents who had professions in the military is 62, 46, 68, 64, 57. Why does it not make sense to construct a histogram for this data set?

With a data set that is so small, the true nature of the distribution cannot be seen with a histogram. Your answer is correct.C.

n a graph, if one or both axes begin at some value other than zero, the differences are exaggerated. This bad graphing method is known as a nonzero axis.

X Nice Work! Using an axis that does not begin at zero can create an incorrect impression that small differences are substantial.

Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Treating 200 men with a special shampoo and recording Yes if they experience anyTreating 200 men with a special shampoo and recording Yes if they experience any burning or No otherwiseburning or No otherwise Choose the correct answer below.

Yea Because all 4 requirements are satisfied.

Determine whether the distribution is a discrete probability distribution. x P(x) 0 0.160.16 1 0.210.21 2 0.260.26 3 0.210.21 4 0.160.16

Yeas the probabilities sum to 1 and are all between 0 and 1 inclusive

Determine whether the given procedure results in a binomial distribution. If it is not binomial, identify the requirements that are not satisfied. Surveying 100 teenagers and recording if they have ever committed a crimeSurveying 100 teenagers and recording if they have ever committed a crime nothing

Yes because all 4 requirements are satisfied

Determine whether the value is from a discrete or continuous data set. Weight of gravel in a pile is 120 lbWeight of gravel in a pile is 120 lb Is the value from a discrete or continuous data set? Continuous

You answered DiscreteDiscrete. The correct answer is ContinuousContinuous because the value for the "weight of gravel in a pile""weight of gravel in a pile" is one of infinitely many possibleone of infinitely many possible valuesvalues and thoseand those values cannot be counted.

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of textbook authors now sitting at a computernumber of textbook authors now sitting at a computer b. The number of fish caught during a fishing tournamentnumber of fish caught during a fishing tournament c. The gender of college studentsgender of college students d. The time it takes for a light bulb to burn outtime it takes for a light bulb to burn out e. The amount of snowfall in December in City Upper Aamount of snowfall in December in City A f. The number of light bulbs that burn out in the next week in a room with 18 bulbs

a - Discrete b - Discrete c- it is not random d- continuous e - continuous f - discrete

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The square footage of a housesquare footage of a house b. The number of bald eagles in a countrynumber of bald eagles in a country c. The eye color of people on commercial aircraft flightseye color of people on commercial aircraft flights d. The number of textbook authors now sitting at a computernumber of textbook authors now sitting at a computer e. The time required to download a file from the Internettime required to download a file from the Internet f. The number of statistics students now reading a book

a - continuous b - discrete c - not random d - discrete e - continuous F- discrete

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of textbook authors now sitting at a computernumber of textbook authors now sitting at a computer b. The square footage of a housesquare footage of a house c. The political party affiliation of adults in the United Statespolitical party affiliation of adults in the United States d. The time it takes for a light bulb to burn outtime it takes for a light bulb to burn out e. The number of people in a restaurant that has a capacity of 300number of people in a restaurant that has a capacity of 300 f. The distance a baseball travels in the air after being hitdistance a baseball travels in the air after being hit a. Is the number of textbook authors now sitting at a computernumber of textbook authors now sitting at a computer a discrete random variable, a continuous random variable, or not a random variable? A. It is a continuouscontinuous random variable. B. It is a discretediscrete random variable. Your answer is correct.C. It is not a random variable. b. Is the square footage of a housesquare footage of a house a discrete random variable, a continuous random variable, or not a random variable? A. It is a continuouscontinuous random variable. Your answer is correct.B. It is a discretediscrete random variable. C. It is not a random variable c. Is the political party affiliation of adults in the United Statespolitical party affiliation of adults in the United States a discrete random variable, a continuous random variable, or not a random variable? A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable. Your answer is correct. d. Is the time it takes for a light bulb to burn outtime it takes for a light bulb to burn out a discrete random variable, a continuous random variable, or not a random variable? A. It is a discretediscrete random variable. B. It is a continuouscontinuous random variable. Your answer is correct.C. It is not a random variable. e. Is the number of people in a restaurant that has a capacity of 300number of people in a restaurant that has a capacity of 300 a discrete random variable, a continuous random variable, or not a random variable?

a - discrete b - continuous c - not random d - Continuous e -Discrete f - Continuous

Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of bald eagles in a countrynumber of bald eagles in a country b. The height of a randomly selected giraffeheight of a randomly selected giraffe c. The political party affiliation of adults in the United Statespolitical party affiliation of adults in the United States d. The number of textbook authors now sitting at a computernumber of textbook authors now sitting at a computer e. The number of free dash throw attempts before the first shot is madenumber of free-throw attempts before the first shot is made f. The number of people in a restaurant that has a capacity of 150

a- Discrete b- Continuous C- Not a random D- Discrete E- Discrete F- Discrete

Refer to the table below. Given that 2 of the 240240 subjects are randomly selected, complete parts (a) and (b). Group O A B AB Type Rh Superscript plusRh+ 8686 6363 2222 2626 Rh Superscript minusRh− 1616 1414 66 7

a. Assume that the selections are made with replacement. What is the probability that the 2 selected subjects are both group ABAB and type Rh Superscript plusRh+? . 0117.0117 (Round to four decimal places as needed.) b. Assume the selections are made without replacement. What is the probability that the 2 selected subjects are both group ABAB and type Rh Superscript plusRh+? . 0113.0113 (Round to four decimal places as needed.)

In a clinical trial of a drug used to help subjects stop smoking, 818818 subjects were treated with 1 mg1 mg doses of the drug. That group consisted of 3232 subjects who experienced nausea. The probability of nausea for subjects not receiving the treatment was 0.01120.0112. Complete parts (a) through (c).

a. Assuming that the drug has no effect, so that the probability of nausea was 0.01120.0112, find the mean and standard deviation for the numbers of people in groups of 818818 that can be expected to experience nausea. The mean is 9.29.2 people. (Round to one decimal place as needed.) The standard deviation is 33 people. (Round to one decimal place as needed.) b. Based on the result from part (a), is it unusual to find that among 818818 people, there are 3232 who experience nausea? Why or why not? - It is unusual because 3232 is outside the range of usual values. Based on the preceding results, does nausea appear to be an adverse reaction that should be of concern to those who use the drug? - The drug does appear to be the cause of some nausea. Since the nausea rate is still quite low (about 44%), it appears to be an adverse reaction that does not occur very often.

A candy company claims that 1010% of its plain candies are orange, and a sample of 100100 such candies is randomly selected.

a. Find the mean and standard deviation for the number of orange candies in such groups of 100100. muμequals= 1010 sigmaσequals= 33 (Round to one decimal place as needed.) b. A random sample of 100100 candies contains 99 orange candies. Is this result unusual? Does it seem that the claimed rate of 1010% is wrong? No because 9 is within the range of usual values. Thus, the claimed rate of 10 %10% is not necessarilynot necessarily wrong.

A government agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages. In standard English text, a particular letter is used at a rate of 7.97.9%.

a. Find the mean and standard deviation for the number of times this letter will be found on a typical page of 35003500 characters. muμequals= 276.5276.5 sigmaσequals= 1616 (Round to one decimal place as needed.) b. In an intercepted message, a page of 35003500 characters is found to have the letter occurring 321321 times. Is this unusual? Yes because 321 is greater than the max usual value

In a region, there is a 0.80.8 probability chance that a randomly selected person of the population has brown eyes. Assume 1414 people are randomly selected. Complete parts (a) through (d) below.

a. Find the probability that all of the selected people have brown eyes. The probability that all of the 1414 selected people have brown eyes is 0.0440.044. (Round to three decimal places as needed.) b. Find the probability that exactly 1313 of the selected people have brown eyes. The probability that exactly 1313 of the selected people have brown eyes is 0.1540.154. (Round to three decimal places as needed.) c. Find the probability that the number of selected people that have brown eyes is 1212 or more. The probability that the number of selected people that have brown eyes is 1212 or more is 0.4480.448. (Round to three decimal places as needed.) d. If 1414 people are randomly selected, is 1212 an unusually high number for those with brown eyes? - No, because the probability that 1212 or more of the selected people have brown eyes is greatergreater than 0.05.

The capacity of an elevator is 1212 people or 19321932 pounds. The capacity will be exceeded if 1212 people have weights with a mean greater than 1932 divided by 12 equals 161 pounds.1932/12=161 pounds. Suppose the people have weights that are normally distributed with a mean of 169 lb169 lb and a standard deviation of 31 lb31 lb.

a. Find the probability that if a person is randomly selected, his weight will be greater than 161161 pounds. The probability is approximately 0.60180.6018. (Round to four decimal places as needed.) b. Find the probability that 1212 randomly selected people will have a mean that is greater than 161161 pounds. The probability is approximately 0.81430.8143. (Round to four decimal places as needed.) c. Does the elevator appear to have the correct weight limit? Why or why not? No, there is a good chance that 1212 randomly selected people will exceed the elevator capacity.

Which word is associated with multiplication when computing probabilities? Choose the correct answer below.

and

Which of the following groups of terms can be used interchangeably when working with normal distributions?

areas, probability, and relative frequencies

The capacity of an elevator is 1515 people or 24602460 pounds. The capacity will be exceeded if 1515 people have weights with a mean greater than 2460 divided by 15 equals 164 pounds.2460/15=164 pounds. Suppose the people have weights that are normally distributed with a mean of 173 lb173 lb and a standard deviation of 26 lb26 lb.

a. Find the probability that if a person is randomly selected, his weight will be greater than 164164 pounds. The probability is approximately 0.63540.6354. (Round to four decimal places as needed.) b. Find the probability that 1515 randomly selected people will have a mean that is greater than 164164 pounds. The probability is approximately 0.91000.9100. (Round to four decimal places as needed.) c. Does the elevator appear to have the correct weight limit? Why or why not? No, there is a good chance that 1515 randomly selected people will exceed the elevator capacity.

A TV show, Lindsay and Tobias, recently had a share of 2020, meaning that among the TV sets in use, 2020% were tuned to that show. Assume that an advertiser wants to verify that 2020% share value by conducting its own survey, and a pilot survey begins with 1414 households having TV sets in use at the time of a Lindsay and Tobias broadcast.

a. Find the probability that none of the households are tuned to Lindsay and Tobias. . 044.044 (Round to three decimal places as needed.) b. Find the probability that at least one household is tuned to Lindsay and Tobias. . 956.956 (Round to three decimal places as needed.) c. Find the probability that at most one household is tuned to Lindsay and Tobias. . 198.198 (Round to three decimal places as needed.) d. If at most one household is tuned to Lindsay and Tobias, does it appear that the 2020% share value is wrong? Why or why not? - NoNo, because with a 2020% rate, the probability of at most one household is greatergreater than 0.05.

Researchers conducted a study to determine whether there were significant differences in graduation rates between medical students admitted through special programs and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 9191% for the medical students admitted through special programs in all medical schools. Complete parts (a) and (b) below.

a. If 1010 of the students admitted through special programs are randomly selected, find the probability that at least 99 of them graduated. The probability that at least 99 of the 1010 students graduated is . 775.775. (Round to three decimal places as needed.) b. Suppose a medical school has 1010 students in one of the special programs of its medical program. Does the probability calculated in part (a) apply to these students? -No, because the students admitted through a single special program at a specific medical school are not a random sample.

n airliner carries 250250 passengers and has doors with a height of 7575 in. Heights of men are normally distributed with a mean of 69.069.0 in and a standard deviation of 2.82.8 in. Complete parts (a) through (d). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is . 9838.9838. (Round to four decimal places as needed.) b. If half of the 250250 passengers are men, find the probability that the mean height of the 125125 men is less than 7575 in. The probability is 11. (Round to four decimal places as needed.)

a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is . 9838.9838. (Round to four decimal places as needed.) b. If half of the 250250 passengers are men, find the probability that the mean height of the 125125 men is less than 7575 in. The probability is 11. c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend. When considering the comfort and safety of passengers, why are women ignored in this case? A. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120120 lb and 181181 lb. The new population of pilots has normally distributed weights with a mean of 129 lb129 lb and a standard deviation of 30.5 lb30.5 lb.

a. If a pilot is randomly selected, find the probability that his weight is between 120120 lb and 181181 lb. The probability is approximately 0.57190.5719. (Round to four decimal places as needed.) b. If 3131 different pilots are randomly selected, find the probability that their mean weight is between 120120 lb and 181181 lb. The probability is approximately 0.94980.9498. (Round to four decimal places as needed.) c. When redesigning the ejection seat, which probability is more relevant? A. Part (a) because the seat performance for a single pilot is more important.

Based on a survey, for women aged 18 to 24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.9114.9 and a standard deviation of 13.113.1. Complete parts (a) through (c).

a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 110110. 0.64580.6458 (Round to four decimal places as needed.) b. If 55 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 110110. 0.79850.7985 (Round to four decimal places as needed.) c. Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be used? Since the original population is normally distributed, the sampling distribution of sample means will be normally distributed for any sample size.

Based on a survey, for women aged 18 to 24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8114.8 and a standard deviation of 13.113.1. Complete parts (a) through (c).

a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 120120. 0.34570.3457 (Round to four decimal places as needed.) b. If 33 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 120120. 0.24590.2459 (Round to four decimal places as needed.) c. Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be used? Since the original population is normally distributed, the sampling distribution of sample means will be normally distributed for any sample size.

What conditions would produce a negative z-score?

a z-score corresponding to an area located entirely in the left side of the curve

a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 120120. 0.34790.3479 (Round to four decimal places as needed.) b. If 55 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 120120. 0.19100.1910 (Round to four decimal places as needed.) c. Given that part (b) involves a sample size that is not larger than 30, why can the central limit theorem be used? Since the original population is normally distributed, the sampling distribution of sample means will be normally distributed for any sample size.

Assume that a company hires employees on Mondays comma Tuesdays comma or WednesdaysMondays, Tuesdays, or Wednesdays nothingwith equal likelihood. Complete parts (a) through (c) below.

a. If two different employees are randomly selected, what is the probability that they were both hired on a Mondaya Monday? The probability is one ninth 1 9. (Type an integer or a simplified fraction.) b. If two different employees are randomly selected, what is the probability that they were both hired on the same day of the weekday of the week? The probability is one third 1 3. (Type an integer or a simplified fraction.) c. What is the probability that 77 people in the same department were all hired on the same day of the weekday of the week? Is such an event unlikely? The probability is StartFraction 1 Over 729 EndFraction 1 729. (Type an integer or a simplified fraction.) Is such an event unlikely? Yes, because the probability that all 77 people were hired on the same day of the weekday of the week nothing is less than or equal toless than or

Men's heights are normally distributed with mean 68.768.7 in and standard deviation of 2.8 in.2.8 in. Women's heights are normally distributed with mean 63.463.4 in and standard deviation of 2.52.5 in. The standard doorway height is 8080 in. a. What percentage of men are too tall to fit through a standard doorway without bending, and what percentage of women are too tall to fit through a standard doorway without bending? b. If a statistician designs a house so that all of the doorways have heights that are sufficient for all men except the tallest 5%, what doorway height would be used?

a. The percentage of men who are too tall to fit through a standard door without bending is 0.000.00%. (Round to two decimal places as needed.) The percentage of women who are too tall to fit through a standard door without bending is 0.000.00%. (Round to two decimal places as needed.) b. The statistician would design a house with doorway height 73.373.3 in.

a. The percentage of men who are too tall to fit through a standard door without bending is 0.010.01%. (Round to two decimal places as needed.) The percentage of women who are too tall to fit through a standard door without bending is 00%. (Round to two decimal places as needed.) b. The statistician would design a house with doorway height 73.373.3 in.

Men's heights are normally distributed with mean 7070 in and standard deviation of 2.8 in.2.8 in. Women's heights are normally distributed with mean 6464 in and standard deviation of 2.52.5 in. The standard doorway height is 8080 in. a. What percentage of men are too tall to fit through a standard doorway without bending, and what percentage of women are too tall to fit through a standard doorway without bending? b. If a statistician designs a house so that all of the doorways have heights that are sufficient for all men except the tallest 5%, what doorway height would be used?

a. The percentage of men who are too tall to fit through a standard door without bending is 0.020.02%. (Round to two decimal places as needed.) The percentage of women who are too tall to fit through a standard door without bending is 0.000.00%. (Round to two decimal places as needed.) b. The statistician would design a house with doorway height 74.674.6 in. (Round to the nearest tenth as needed.)

A survey found that women's heights are normally distributed with mean 63.463.4 in and standard deviation 2.42.4 in. A branch of the military 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 this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

a. The percentage of women who meet the height requirement is 98.7898.78%. (Round to two decimal places as needed.) Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? A. No, because only a small percentage of women are not allowed to join this branch of the military because of their height. b. For the new height requirements, this branch of the military requires women's heights to be at least 57.857.8 in and at most 68.368.3 in.

A survey found that women's heights are normally distributed with mean 63.663.6 in and standard deviation 2.22.2 in. A branch of the military 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 this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

a. The percentage of women who meet the height requirement is 99.45% No, because only a small percentage of women are not allowed to join this branch of the military because of their height. b. For the new height requirements, this branch of the military requires women's heights to be at least 58.558.5 in and at most 68.1 in.

If a gambler places a bet on the number 7 in roulette, he or she has a 1/38 probability of winning. a. Find the mean and standard deviation for the number of wins of gamblers who bet on the number 7 three hundredthree hundred times. b. Would 0 wins in three hundredthree hundred bets be an unusually low number of wins?

a. The value of the mean is muμequals= 7.97.9. (Round to one decimal place as needed.) The value of the standard deviation is sigmaσequals= 2.82.8. (Round to one decimal place as needed.) b. Would 0 wins in 300300 bets be an unusually low number of wins? Yes because 0 is below the minimum usual value

A brand name has aa 5050% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 44 randomly selected consumers. Complete parts (a) through (d) below.

a. What is the probability that exactly 33 of the selected consumers recognize the brand name? The probability that exactly 33 of the 44 consumers recognize the brand name is 0.2500.250. (Round to three decimal places as needed.) b. What is the probability that all of the selected consumers recognize the brand name? The probability that all of the selected consumers recognize the brand name is 0.0630.063. (Round to three decimal places as needed.) c. What is the probability that at least 33 of the selected consumers recognize the brand name? The probability that at least 33 of the selected consumers recognize the brand name is 0.3130.313. (Round to three decimal places as needed.) d. If 44 consumers are randomly selected, is 33 an unusually high number of consumers that recognize the brand name? No, because the probability that 33 or more of the selected consumers recognize the brand name is greatergreater than 0.05.

A brand name has aa 5050% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 55 randomly selected consumers. Complete parts (a) through (d) below.

a. What is the probability that exactly 44 of the selected consumers recognize the brand name? The probability that exactly 44 of the 55 consumers recognize the brand name is 0.1560.156. (Round to three decimal places as needed.) b. What is the probability that all of the selected consumers recognize the brand name? The probability that all of the selected consumers recognize the brand name is 0.0310.031. (Round to three decimal places as needed.) c. What is the probability that at least 44 of the selected consumers recognize the brand name? The probability that at least 44 of the selected consumers recognize the brand name is 0.1880.188. (Round to three decimal places as needed.) d. If 55 consumers are randomly selected, is 44 an unusually high number of consumers that recognize the brand name? - No, because the probability that 44 or more of the selected consumers recognize the brand name is greatergreater than 0.05.

A brand name has aa 6060% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 66 randomly selected consumers. Complete parts (a) through (d) below.

a. What is the probability that exactly 55 of the selected consumers recognize the brand name? The probability that exactly 55 of the 66 consumers recognize the brand name is 0.1870.187. (Round to three decimal places as needed.) b. What is the probability that all of the selected consumers recognize the brand name? The probability that all of the selected consumers recognize the brand name is 0.0470.047. (Round to three decimal places as needed.) c. What is the probability that at least 55 of the selected consumers recognize the brand name? The probability that at least 55 of the selected consumers recognize the brand name is 0.2330.233. (Round to three decimal places as needed.) d. If 66 consumers are randomly selected, is 55 an unusually high number of consumers that recognize the brand name? No, because the probability that 55 or more of the selected consumers recognize the brand name is greatergreater than 0.05.

Assume that adults have IQ scores that are normally distributed with a mean of 105105 and a standard deviation 1515. Find Upper P 15P15, which is the IQ score separating the bottom 1515% from the top 8585%.

he IQ score that separates the bottom 1515% from the top 8585% is Upper P 15P15equals= 89.4589.45.

A brand name has aa 6060% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 77 randomly selected consumers. Complete parts (a) through (d) below.

a. What is the probability that exactly 66 of the selected consumers recognize the brand name? The probability that exactly 66 of the 77 consumers recognize the brand name is 0.1310.131. (Round to three decimal places as needed.) b. What is the probability that all of the selected consumers recognize the brand name? The probability that all of the selected consumers recognize the brand name is 0.0280.028. (Round to three decimal places as needed.) c. What is the probability that at least 66 of the selected consumers recognize the brand name? The probability that at least 66 of the selected consumers recognize the brand name is 0.1590.159. (Round to three decimal places as needed.) d. If 77 consumers are randomly selected, is 66 an unusually high number of consumers that recognize the brand name? NoNo, because the probability that 66 or more of the selected consumers recognize the brand name is greatergreater than 0.05.

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 7.67.6% daily failure rate. Complete parts (a) through (d) below.

a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? . 076.076 (Round to three decimal places as needed.) b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? . 00578.00578 (Round to five decimal places as needed.) c. What is the probability of not being awakened if the student uses three independent alarm clocks? . 00044.00044 (Round to five decimal places as needed.) Do the second and third alarm clocks result in greatly improved reliability? Yes, because total malfunction would not be impossible, but it would be unlikely.

If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg. a. Construct a similar sample space for the possible hair colorhair color outcomes (using b for brown dash haired and r for red dash headedb for brown-haired and r for red-headed) of two children. b. Assuming that the outcomes listed in part (a) were equally likely, find the probability of getting two brown dash hairedbrown-haired children. c. Find the probability of getting exactly one brown dash hairedbrown-haired child and one red dash headedred-headed child.

a. What is the sample space? bb comma br comma rb comma rrbb,br,rb,rr (Use a comma to separate answers as needed.) b. Find the probability of getting two brown dash hairedbrown-haired children . 25.25 (Type an exact answer.) c. Find the probability of getting one brown dash hairedbrown-haired child and one red dash headedred-headed child. . 5.5 (Type an exact answer.)

Several psychology students are unprepared for a surprise true/false test with 1313 questions, and all of their answers are guesses. a. Find the mean and standard deviation for the number of correct answers for such students. b. Would it be unusual for a student to pass by guessing (which requires getting at least 88 correct answers)? Why or why not?

a. muμequals= 6.56.5 sigmaσequals= 1.81.8 b. No because 8 is within the range of usual values

Several psychology students are unprepared for a surprise true/false test with 1414 questions, and all of their answers are guesses. a. Find the mean and standard deviation for the number of correct answers for such students. b. Would it be unusual for a student to pass by guessing (which requires getting at least 1010 correct answers)? Why or why not?

a. muμequals= 77 sigmaσequals= 1.91.9 (Round to one decimal place as needed.) b. Choose the correct answer below. - No because 10 is within the range of usual values

When using the _______ always be careful to avoid double-counting outcomes.

addition rule

Which word is associated with multiplication when computing probabilities?

and

A survey found that women's heights are normally distributed with mean 63.663.6 in and standard deviation 2.32.3 in. A branch of the military 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 this branch of the military because they are too short or too tall? b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?

b. For the new height requirements, this branch of the military requires women's heights to be at least 58.258.2 in and at most 68.368.3 in. (Round to one decimal place as needed.) No, because only a small percentage of women are not allowed to join this branch of the military because of their height.

Determine whether the given value is a statistic or a parameter. Upper A sample of employees is selected and it is found that 65 % own a computer.A sample of employees is selected and it is found that 65% own a computer. Choose the correct statement below

because the value is a numerical measurement describing a characteristic of a samplesample.

A _______ is any event combining two or more simple events.

compound event

Determine whether the value is from a discrete or continuous data set. Time to learn a song is 4 hoursTime to learn a song is 4 hours Is the value from a discrete or continuous data set?

continuous

Determine whether the value is from a discrete or continuous data set. Number of bacteria in a petri dish is 12 comma 120Number of bacteria in a petri dish is 12,120 Is the value from a discrete or continuous data set?

discrete

Events that are _______ cannot occur at the same time.

disjoint

The classical approach to probability requires that the outcomes are _______.

equally likely

equals= 105105 sigmaσequals= 5.65.6 (Round to one decimal place as needed.) mu minus 2 sigmaμ−2σequals= 93.893.8 (Round to one decimal place as needed.) mu plus 2 sigmaμ+2σequals= 116.2116.2 (Round to one decimal place as needed.)

Determine whether the given description corresponds to an observational study or an experiment. In a study of 420420 menmen with a particular disease, the subjects were injected with vitamins towere injected with vitamins to determine if the vitamins have an effect on the disease.determine if the vitamins have an effect on the disease. Does the given description correspond to an observational study or an experiment?

he given description corresponds to an experimentan experiment.

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. Ages of children: 3 comma 4 comma 5 comma 6 comma and 7Ages of children: 3, 4, 5, 6, and 7 Choose the correct answer below.

he nominal level of measurement is characterized by data that consist of names, labels, or categories only. Data are at the ordinal level of measurement if they can be arranged in some order. The interval level of measurement is like the ordinal level, with the additional property that the difference between any two data values is meaningful. The ratio level of measurement is the interval level with the additional property that there is also a natural zero starting point.

The table below summarizes results from a study of people who refused to answer survey questions. If one of the subjects is randomly selected, what is the probability that the selected person refused to answer? Does the probability value suggest that refusals are a problem for pollsters? Age 18-21 22-29 30-39 40-49 50-59 60 and over Responded 7878 260260 250250 141141 143143 207207 Refused

he probability that a randomly selected person refused to answer is . 14.14. Yes, the refusal rate is above 10%. This may suggest that the sample may not be representative of the population.

Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees0° and standard deviation of 1.00degrees°C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 81P81, the 81 st81st percentile. This is the temperature reading separating the bottom 81 %81% from the top 19 %.

he temperature for Upper P 81P81 is approximately 0.880.88degrees°.

selections made with replacement are considered to be _______.

independent

A genetic experiment with peas resulted in one sample of offspring that consisted of 425425 green peas and 154154 yellow peas. Construct a 9595% confidence interval to estimate of the percentage of yellow peas.

less than<pless than< 0.3020.302

Which of the following is NOT a value in the 5-number summary?

mean

Five males with a particular genetic disorder have one child each. The random variable x is the number of children among the five who inherit the genetic disorder. Determine whether the table describes a probability distribution. If it does, find the mean and standard deviation. x 0 1 2 3 4 5 P(x) 0.34870.3487 0.40890.4089 0.19190.1919 0.04500.0450 0.00530.0053 0.00020.0002

mean = 0.9 SD = 0.9

Assume that a procedure yields a binomial distribution with 66 trials and a probability of success of 0.700.70. Use a binomial probability table to find the probability that the number of successes is exactly 00.

successes = 0 = .001

Do one of the following, as appropriate. (a) Find the critical value z Subscript alpha divided by 2zα/2, (b) find the critical value t Subscript alpha divided by 2tα/2, (c) state that neither the normal nor the t distribution applies. Confidence level 9898%; nequals=1717; sigma is unknownσ is unknown; population appears to be normally distributed.

t = 2.583

When someone buys a ticket for an airline flight, there is a 0.09870.0987 probability that the person will not show up for the flight. A certain jet can seat 2121 passengers. Is it wise to book 2323 passengers for a flight on the jet? Explain.

t is not a wise decision because the probability that there are not enough seats on the jet is . 3224.3224. So, overbooking is not an unlikely event.

To construct a confidence interval using the given confidence level, do whichever of the following is appropriate. (a) Find the critical value z Subscript alpha divided by 2zα/2, (b) find the critical value t Subscript alpha divided by 2tα/2, or (c) state that neither the normal nor the t distribution applies. 9595%; nequals=300300; sigma is unknownσ is unknown; population appears to be skewed

t= 1.968

For data sets having a distribution that is approximately bell-shaped, _______ states that about 95% of all data values fall within two standard deviations from the mean.

the Empirical Rule

As a procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as _______.

the law of large numbers

As a procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as _______.

the law of large numbers.

Assume that women's heights are normally distributed with a mean given by mu equals 62.6 inμ=62.6 in, and a standard deviation given by sigma equals 2.1 inσ=2.1 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 6363 in. (b) If 4646 women are randomly selected, find the probability that they have a mean height less than 6363 in.

the probability is approximately 0.57550.5755. The probability is approximately 0.90180.9018.

Complete the following statement. Upper P left parenthesis Upper A or Upper B right parenthesisP(A or B) indicates _______.

the probability that in a single trial, event A occurs, event B occurs, or they both occur.

Complete the following statement. Upper P left parenthesis Upper A or Upper B right parenthesisP(A or B) indicates _______. Choose the correct answer below.

the probability that in a single trial, event A occurs, event B occurs, or they both occur.

Upper P left parenthesis Upper A or Upper B right parenthesisP(A or B) indicates _______.

the probability that in a single trial, event A occurs, event B occurs, or they both occur.

the notation P(zless than<a) denotes _______.

the probability that the z-score is less than a.

Where would a value separating the top 15% from the other values on the graph of a normal distribution be found?

the right side of the horizontal scale of the graph

The area in any normal distribution bounded by some score x is the same as the area bounded by the equivalent z-score in the standard normal distribution.

true

A data value is considered _______ if its z-score is less than minus−2 or greater than 2.

unusual

A certain group of women has a 0.030.03% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness? What is the probability that the woman selected does not have red/green color blindness?

.9997

Assume that women's heights are normally distributed with a mean given by mu equals 62.5 inμ=62.5 in, and a standard deviation given by sigma equals 2.9 inσ=2.9 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 6363 in. (b) If 4444 women are randomly selected, find the probability that they have a mean height less than 6363 in.

(a) The probability is approximately . 5675.5675. (Round to four decimal places as needed.) (b) The probability is approximately . 8729.8729.

Assume that women's heights are normally distributed with a mean given by mu equals 62.4 inμ=62.4 in, and a standard deviation given by sigma equals 2.4 inσ=2.4 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 6363 in. (b) If 4343 women are randomly selected, find the probability that they have a mean height less than 6363 in.

(a) The probability is approximately 0.59870.5987. (Round to four decimal places as needed.) (b) The probability is approximately 0.94940.9494.

Heights of men on a baseball team have a bell-shaped distribution with a mean of 175 cm175 cm and a standard deviation of 6 cm6 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 157157 cm and 193193 cm b. 163163 cm and 187187 cm

99.7% of the men are between 157157 cm and 193193 cm. 95% of the men are between 163163 cm and 187187 cm.

Decide whether the following two events are disjoint. 1. Randomly selecting someone who owns a carRandomly selecting someone who owns a car 2. Randomly selecting a married maleRandomly selecting a married male Are the two events disjoint?

No, because the events cancan occur at the same time.

Listed below are the arrival delay times (in minutes) of randomly selected airplane flights from one airport to another. Negative values correspond to flights that arrived early before the scheduled arrival time, and positive values represent lengths of delays. Find the range, variance, and standard deviation for the set of data. Some of the sample values are negative, but can the standard deviation ever be negative?

No, because the squared value in the standard deviation formula cannot be negative.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. FiveFive cards are selected from a standard 52-card deck without replacement. The number of fivesfives selected is recorded.

No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.

The capacity of an elevator is 1010 people or 16301630 pounds. The capacity will be exceeded if 1010 people have weights with a mean greater than 1630 divided by 10 equals 163 pounds.1630/10=163 pounds. Suppose the people have weights that are normally distributed with a mean of 172 lb172 lb and a standard deviation of 34 lb34 lb.

No, there is a good chance that 1010 randomly selected people will exceed the elevator capacity.

n a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, 219219 answered "none," 291291 said "one," 365365 said "two," 140140 said "three," and 110110 responded with four or more. A survey respondent is selected at random. Find the probability that his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05.

P(four or more cell phones)equals= . 098 Is it unlikely for a household to have four or more cell phones in use? , because the probability of a respondent with four or more cell phones in use is greater thangreater than 0.05.

The following data summarizes results from 979979 pedestrian deaths that were caused by accidents. If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated.

P(pedestrian was intoxicated or driver was intoxicated)equals= . 443 (Round to three decimal places as needed.)

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 9494 people in the 18-21 age bracket and finds that 6464 of them respond and 3030 refuse to respond. When 287287 people in the 22-29 age bracket are contacted, 271271 respond and 1616 refuse to respond. Suppose that one of the 381381 people is randomly selected. Find the probability of getting someone in the 22 dash 2922-29 age bracket or someone who refused to respondrefused to respond.

P(person is in the 22 dash 2922-29 age bracket or refused to respondrefused to respond)equals= . 832

The following data summarizes results from 10001000 pre-employment drug screening tests. If one of the test subjects is randomly selected, find the probability that the subject had a positive test result or a negative test result.

P(subject had a positive test result or a negative test result)equals= 1 (Simplify your answer.)

Decide whether the following two events are disjoint. 1. Randomly selecting someone treated with a certain medicationRandomly selecting someone treated with a certain medication 2. Randomly selecting someone who received no medicationRandomly selecting someone who received no medication Are the two events disjoint?

Yes, because the events cannotcannot occur at the same time.

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. An experimental drug is administered to 140140 randomly selected individuals, with the number of individuals responding favorably recorded.

Yes, because the experiment satisfies all the criteria for a binomial experiment.

Assume that women's heights are normally distributed with a mean given by mu equals 62.4 inμ=62.4 in, and a standard deviation given by sigma equals 1.7 inσ=1.7 in. (a) If 1 woman is randomly selected, find the probability that her height is less than 6363 in. (b) If 3131 women are randomly selected, find the probability that they have a mean height less than 6363 in.

a) The probability is approximately 0.63790.6379. (Round to four decimal places as needed.) (b) The probability is approximately 0.97530.9753. (Round to four decimal places as needed.)

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