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mathematics
statistics
Elementary Statistics 12th Edition Mario F. Triola - Solutions
Given the results described in Exercise, is the mean of 140.0 executives expressed with m or x? Explain why the mean of 140.0 executives is a parameter instead of a statistic.
Random guesses are made for the 60 multiple-choice questions on the math portion of the ACT test, so n = 60 and p = 1>5 (because each question has possible answers of a, b, c, d, e, and only one of them is correct).
In an analysis of preliminary test results from the XSORT gender selection method, 14 babies are born and it is assumed that 50% of babies are girls, so n = 14 and p = 0.5.
In a Gallup poll of 1013 randomly selected adults, 66% said that they worry about identity theft, so n = 1013 and p = 0.66.
In a clinical trial of the cholesterol drug Lipitor, 94 subjects were treated with 80 mg of Lipitor, and 6.4% of them developed headaches, so n = 94 and p = 0.064.
In a test of the YSORT method of gender selection, 291 babies are born to couples trying to have baby boys, and 239 of those babies are boys (based on data from the Genetics & IVF Institute). a. If the gender-selection method has no effect and boys and girls are equally likely, find the mean and
When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 580 peas, and Mendel theorized that 25% of them would be yellow peas. a. If Mendel’s theory is correct, find the mean and standard deviation for the numbers of yellow peas in such groups of 580
Mars, Inc. claims that 20% of its M&M plain candies are orange, and a sample of 100 such candies is randomly selected. a. Find the mean and standard deviation for the number of orange candies in such groups of 100. b. Data Set 20 in Appendix B consists of a random sample of 100 M&Ms, including 25
Mars, Inc. claims that 14% of its M&M plain candies are yellow, and a sample of 100 such candies is randomly selected. a. Find the mean and standard deviation for the number of yellow candies in such groups of 100. b. Data Set 20 in Appendix B consists of a random sample of 100 M&Ms, including 8
In a study of 420,095 cell phone users in Denmark, it was found that 135 developed cancer of the brain or nervous system. If we assume that the use of cell phones has no effect on developing such cancer, then the probability of a person having such a cancer is 0.000340. a. Assuming that cell phones
Nine-year-old Emily Rosa conducted this test: A professional touch therapist put both hands through a cardboard partition and Emily would use a coin flip to randomly select one of the hands. Emily would place her hand just above the hand of the therapist, who was then asked to identify the hand
The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In Standard English text, the letter r is used at a rate of 6%. a. Find the mean and standard deviation for the
The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages that are sent as ciphered text. In standard English text, the letter e is used at a rate of 12.7%. a. Find the mean and standard deviation for the
Based on a Harris poll of 370 adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. a. For randomly selected groups of 370 adults who regret getting tattoos, find the mean and standard deviation for the number who say that they were too young when they got
If you place a bet on the number 7 in roulette, you have a 1>38 probability of winning.a. Find the mean and standard deviation for the number of wins for people who bet on the number 7 fifty times.b. Would 0 wins in 50 bets be an unusually low number of wins?
For the following questions, ignore leap years. a. For classes of 30 students, find the mean and standard deviation for the number born on the 4th of July. Express results using seven decimal places. b. For a class of 30 students, would 2 be an unusually high number who were born on the 4th of July?
As of this writing, the Powerball lottery is run in 42 states. If you buy one ticket, the probability of winning is 1/195,249,054. If you buy one ticket each week for 50 years, you play this lottery 2600 times. a. Find the mean and standard deviation for the number of wins for people who buy a
In a survey of randomly selected adults, subjects were asked if they could identify at least one current member of the Supreme Court. After obtaining the results, the range rule of thumb was used to find that for randomly selected groups of the same size, the minimum usual number who could identify
A statistics class consists of 10 females and 30 males, and each day, 12 of the students are randomly selected without replacement. Because the sampling is from a small finite population without replacement, the hypergeometric distribution applies. Using the hypergeometric distribution, find the
In analyzing hits by V-1 buzz bombs in World War ii, South London was partitioned in to 576 regions, each with an area of 0.25 km2. A. total of 535 bombs hit the combined area of 576 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In
During a recent 46-year period, New York State had a total of 194 tornadoes that measured 1 or greater on the Fujita scale. Let the random variable x represent the number of such tornadoes to hit New York State in one year, and assume that it has a Poisson distribution. What is the mean number of
Assume that we want to find the probability of getting at least one win when playing the Texas Pick 3 lottery 50 times. For one bet, there is a 1>1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? Why or why
Assume that we plan to play the Texas Pick 3 lottery 100 times. For one bet, there is a 1>1000 probability of winning. If we want to use the Poisson distribution as an approximation to the binomial, are the requirements satisfied? If we use the Poisson distribution to find the probability of 101
Various sources provide different earthquake data, but assume that for a recent 41-year period in the United States, there were 268 earthquakes measured at 6.0 or higher on the Richter scale (based on U.S. Geological Survey data). a. Find the mean number of earthquakes per year. b. Find the
Various sources provide different earthquake data, but assume that for a recent 41-year period in the world, there were 5469 earthquakes measured at 6.0 or higher on the Richter scale (based on U.S. Geological Survey data). a. Find the mean number of earthquakes per year. b. Find the probability
Radioactive atoms are unstable because they have too much energy. When they release their extra energy, they are said to decay. When studying cesium-137, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 977,287 radioactive atoms, so 22,713 atoms decayed during 365
A classical example of the Poisson distribution involves the number of deaths caused by horse kicks to men in the Prussian Army between 1875 and 1894. Data for 14 corps were combined for the 20-year period, and the 280 corps-years included a total of 196 deaths. After finding the mean number of
In Exercise 1 we noted that in analyzing hits by V-1 buzz bombs in World War II, South London was partitioned into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions. a. Find the probability that a randomly selected region had exactly 2 hits. b.
Neuroblastoma, a rare form of malignant tumor, occurs in 11 children in a million, so its probability is 0.000011. Four cases of neuroblastoma occurred in Oak Park, Illinois, which had 12,429 children. a. Assuming that neuroblastoma occurs as usual, find the mean number of cases in groups of 12,429
In the production of chocolate chip cookies, we can consider each cookie to be the specified interval unit required for a Poisson distribution, and we can consider the variable x to be the number of chocolate chips in a cookie. Table 3-1 is included with the Chapter Problemfor Chapter 3, and it
Consider an individual chocolate chip cookie to be the specified interval unit required for a Poisson distribution, and consider the variable x to be the number of chocolate chips in a cookie. Table 3-1 is included with the Chapter Problem for Chapter 3, and it includes the numbers of chocolate
An experiment consists of rolling a single die 12 times and the variable x is the number of times that the outcome is 6. a. Can the Poisson distribution be used to find the probability that the outcome of 6 occurs exactly 3 times? Why or why not? b. If the Poisson distribution is used, is the
Groups of 600 people are randomly selected. Find the mean and standard deviation for the numbers ofpeople with brown eyes in such groups, then use the range rule of thumb to identify the range of usual values for those with brown eyes. For such a group of 600 randomly selected people, is 200 with
When randomly selecting 600 people, the probability of exactly 239 people with brown eyes is P(239) = 0.0331. Also, P(239 or fewer) = 0.484. Which of those two probabilities is relevant for determining whether 239 is an unusually low number of people with brown eyes? Is 239 an unusually low number
Does the table describe a probability distribution? Why or why not?
Find the mean and standard deviation for the random variable x. Use the range rule of thumb to identify the range of usual values for the number of males with tinnitus among four randomly selected males. Is it unusual to get three males with tinnitus among four randomly selected males?
In a study of brand recognition of the Kindle eReader, four consumers are interviewed. If x is the number of consumers in the group who recognize the Kindle brand name, then x can be 0, 1, 2, 3, or 4. If the corresponding probabilities are 0.026, 0.154, 0.346, 0.246, and 0.130, does the given
In the television game show Deal or No Deal, contestant Elna Hindler had to choose between acceptance of an offer of $193,000 or continuing the game. If she continued to refuse all further offers, she would have won one of these five equally likely prizes: $75, $300, $75,000, $500,000, and
Sweepstakes Reader’s Digest ran a sweepstakes in which prizes were listed along with the chances of winning: $1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5,000 (1 chance in 36,667,000), and $2,500 (1 chance in 27,500,000). a.
In the month preceding the creation of this exercise, the author made 18 phone calls in 30 days. No calls were made on 19 days, 1 call was made on 8 days, and 2 calls were made on 5 days. a. Find the mean number of calls per day. b. Use the Poisson distribution to find the probability of no calls
The Organization for Economic Cooperation and Development provided the following mean weekly instruction times (hours) for elementary and high school students in various countries: 22.2 (United States); 24.8 (France); 24.2 (Mexico); 26.9 (China); 23.8 (Japan). Use the five given times for the
In Ohio’s Pick 4 game, you pay $1 to select a sequence of four digits, such as 7709. If you buy only one ticket and win, your prize is $5000 and your net gain is $4999. a. If you buy one ticket, what is the probability of winning? b. Construct a table describing the probability distribution
In the last U.S. Open tennis tournament, there were 611 challenges made by singles players, and 172 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.a. If one of the 611 challenges is randomly selected, what is the probability that it
Gender Gap In recent years, the discrepancy between incomes of women and men has been shrinking, but it continues to exist. The accompanying graph illustrates the current gap. The graph shows that for every $100 earned by men, women earn $82.80 (based on data from the Bureau of Labor Statistics).
The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are randomly selected for applications including the selection of lottery numbers and the selection of telephone numbers to be called as part of a survey. In the following tables, the table at the left summarizes actual results from 100 randomly selected
Based on a USA Today poll, assume that 10% of the population believes that college is no longer a good investment. a. Find the probability that among 16 randomly selected people exactly 4 believe that college is no longer a good investment. b. Find the probability that among 16 randomly selected
A normal distribution is informally described as a probability distribution that is “bell-shaped” when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Between 0.25 and 1.25 Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table A-2,
Between 1.23 and 2.37 Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table A-2,
Between and -2.75 and -2.00 Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table
Between -1.93 and -0.45. Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table
Between -2.20 and 2.50 Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table A-2,
Between -0.62 and 1.78. Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table A-2,
Between −2.11 and 4.00 Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table
Between -3.90 and 2.00. Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table A-2,
About % of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean). Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical
About % of the area is between z = -2 and z = 2 (or within 2 standard deviations of the mean). Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical
About % of the area is between z = − 3 and z = 3 (or within 3 standard deviations of the mean). Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the
About % of the area is between z = -3.5 and z = 3.5 (or within 3.5 standard deviations of the mean). Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the
For bone density scores that are normally distributed with a mean of 0 and a standard deviation of 1, find the percentage of scores that are a. Within 1 standard deviation of the mean. b. More than 2 standard deviations away from the mean. f. Within 1.96 standard deviations of the mean. d. Between
In a continuous uniform distribution, μ = minimum + maximum / 2 and σ = range / √12 a. Find the mean and standard deviation for the distribution of the subway waiting times represented in Figure. b. For a continuous uniform distribution with m = 0 and s = 1, the minimum is -23 and the maximum
Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute (based on Data Set 1 in Appendix B). a. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = (x -
The Wechsler Adult Intelligence Scale is an IQ score obtained through a test, and the scores are normally distributed with a mean of 100 and a standard deviation of 15. A bell-shaped graph is drawn to represent this distribution. a. For the bell-shaped graph, what is the area under the curve? b.
What is the difference between a standard normal distribution and a nonstandard normal distribution?
Random Digits Computers are commonly used to randomly generate digits of telephone numbers to be called when conducting a survey. Can the methods of this section be used to find the probability that when one digit is randomly generated, it is less than 3? Why or why not? What is the probability of
Find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
Find the probability of an IQ less than 85. Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). For a randomly selected adult, find the indicated probability or IQ score. Round IQ scores to the nearest whole
Find the probability of an IQ greater than 70 (the requirement for being a statistics textbook author). Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). For a randomly selected adult, find the indicated
Find the probability that a randomly selected adult has an IQ between 90 and 110 (referred to as the normal range).
Find the probability that a randomly selected adult has an IQ between 110 and 120 (referred to as bright normal). Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). For a randomly selected adult, find the
The U.S. Navy requires that fighter pilots have heights between 62 in. and 78 in. a. Find the percentage of women meeting the height requirement. Are many women not qualified because they are too short or too tall? b. Find the percentage of men meeting the height requirement. Are many men not
The U.S. Air Force requires that pilots have heights between 64 in. and 77 in. a. Find the percentage of women meeting the height requirement. b. Find the percentage of men meeting the height requirement. c. If the Air Force height requirements are changed to exclude only the tallest 3% of men and
Most of the live characters at Disney World have height requirements with a minimum of 4 ft 8 in. and a maximum of 6 ft 3 in. a. Find the percentage of women meeting the height requirement. b. Find the percentage of men meeting the height requirement. c. If the height requirements are changed to
The Gulfstream 100 is an executive jet that seats six, and it has a doorway height of 51.6 in. a. What percentage of adult men can fit through the door without bending? b. What percentage of adult women can fit through the door without bending? c. Does the door design with a height of 51.6 in.
When a water taxi sank in Baltimore’s Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a “worst-case” scenario in which all of the passengers are adult
A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work table, we must consider sitting knee height, which is the distance from the bottom of the feet to the top of
The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. a. One classical use of the normal distribution is inspired by a letter to “Dear Abby” in which a wife claimed to have given birth 308 days after a brief visit from her husband, who
Based on the sample results in Data Set 3 in Appendix B, assume that human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. a. Bellevue Hospital in New York City uses 100.6°F as the lowest temperature considered to be a fever. What percentage
Based on Data Set 16 in Appendix B, assume that Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.184 and a standard deviation of 0.587. a. Earthquakes with magnitudes less than 2.000 are considered “micro earthquakes” that are not felt. What percentage of
Width Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard
The Chapter Problem for Chapter 3 includes Table, which lists the numbers of chocolate chips in Chips Ahoy regular cookies. Those numbers have a distribution that is approximately normal with a mean of 24.0 chocolate chips and a standard deviation of 2.6 chocolate chips. Find P1 and P99. How might
After 1964, quarters were manufactured so that the weights had a mean of 5.67 g and a standard deviation of 0.06 g. Some vending machines are designed so that you can adjust the weights of quarters that are accepted. If many counterfeit coins are found, you can narrow the range of acceptable
Refer to Data Set 1 in Appendix B and use the pulse rates of males. a. Find the mean and standard deviation, and verify that the pulse rates have a distribution that is roughly normal. b. Treating the unrounded values of the mean and standard deviation as parameters and assuming that male pulse
Pepsi Refer to Data Set 19 in Appendix B and use the weights (pounds) of Diet Pepsi. a. Find the mean and standard deviation, and verify that the data have a distribution that is roughly normal. b. Treating the unrounded values of the mean and standard deviation as parameters, and assuming that the
A statistics professor gives a test and finds that the scores are normally distributed with a mean of 40 and a standard deviation of 10. She plans to curve the scores. a. If she curves by adding 35 to each grade, what is the new mean? What is the new standard deviation? b. Is it fair to curve by
There are many situations in which a normal distribution can be used as a good approximation to a random variable that has only discrete values. In such cases, we can use this continuity correction: Represent each whole number by the interval extending from 0.5 below the number to 0.5 above it. The
For the purposes of constructing modified box plots as described in Section 3-4, outliers defined as data values that are above Q3 by an amount greater than 1.5 × IQR or below Q1 by an amount greater than 1.5 × IQR, where IQR is the interquartile range. Using this definition of outliers, find the
Based on recent results, scores on the SAT test are normally distributed with a mean of 1511 and a standard deviation of 312. Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of 5.1. Assume that the two tests use different scales to measure the same
In a recent year, the U.S. Mint in Denver manufactured 270 million quarters. Assume that on each day of production, a sample of 50 quarters is randomly selected, and the mean weight is obtained. a. Given that the population of quarters has a mean weight of 5.67 g, what do you know about the mean of
In a recent year, the U.S. Mint in Denver manufactured 270 million quarters. As part of the mint’s quality control program, samples of quarters are randomly selected each day for detailed inspection to confirm that they meet all required specifications. a. Do you think the quarters are randomly
Many states have a Pick 3 lottery in which three digits are randomly selected each day. Winning requires that you select the same three digits in the same order that they are drawn. Assume that you compute the mean of each set of three selected digits. a. What is the approximate shape of the
Distribution of the Sample Variance a. Find the value of the population variance s2. b. Table describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample variance s2. Then combine values of s2 that are the same, as in Table.
For the following, round results to three decimal places.a. Find the value of the population standard deviation s.b. Table describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample standard deviations. Then combine values
a. Find the value of the population median.b. Table describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample median. Then combine values of the median that are the same, as in Table.c. Find the mean of the sampling
a. For the population, find the proportion of odd numbers.b. Table describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample proportion of odd numbers. Then combine values of the sample proportion that are the same, as in
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