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mathematics
elementary statistics picturing
Elementary Statistics 11th Edition Mario F. Triola - Solutions
Find the mean and standard deviation for the numbers of peas with green pods. Refer to the accompanying table, which describes results from eight offspring peas. The random variable x represents the number of offspring peas with green pods. Probabilities of Numbers of Peas with Green Pods Among 8
In a test of the XSORT method of gender selection, 574 babies are born to couples trying to have baby girls, and 525 of those babies are girls (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
In a test of the YSORT method of gender selection, 152 babies are born to couples trying to have baby boys, and 127 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 plants, one sample of 1064 offspring consisted of 787 plants with long stems and 277 plants with short stems. Mendel theorized that 25% of the offspring plants would have short stems.a. If Mendel’s theory is correct, find the mean and
A headline in USA Today states that “most stay at first job less than 2 years.” That headline is based on an Experience.com poll of 320 college graduates. Among those polled, 78% stayed at their first full-time job less than 2 years.a. Assuming that 50% is the true percentage of graduates who
A Fidelity life insurance company charges $226 for a $50,000 life insurance policy for a 50-year-old female. The probability that such a female survives the year is 0.9968 (based on data from the U.S. Department of Health and Human Services). Assume that the company sells 700 such policies to
a. Find the probability of getting exactly 3 peas with green pods. b. Find the probability of getting 3 or fewer peas with green pods. c. Which probability is relevant for determining whether 3 is an unusually low number of peas with green pods: the result from part (a) or part (b)? d. Is 3 an
a. Find the probability of getting exactly 7 peas with green pods. b. Find the probability of getting 7 or more peas with green pods. c. Which probability is relevant for determining whether 7 is an unusually high number of peas with green pods: the result from part (a) or part (b)? d. Is 7 an
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use Table A-1 to find the probability of x successes given the probability p of success on a given trial.n = 2 x = 1 p = 0.30
Nielsen Media Research conducts surveys to determine the proportion of households tuned to television shows. Assume that a different random sample of 5000 households is obtained each week. If the proportion of households tuned to 60 Minutes is recorded for each Sunday during the course of two
Assume that the population of human body temperatures has a mean of 98.6°F, as is commonly believed. Also assume that the population standard deviation is 0.62°F (based on data from University of Maryland researchers). If a sample of size n = 106 is randomly selected, find the probability of
What is the standard error of the mean?
A normal distribution is informally described as a probability distribution that is “bell-shaped” when graphed. Describe the “bell shape.”
In a study of incomes of individual adults in the United States, it is observed that many people have no income or very small incomes, while there are very few people with extremely large incomes, so a graph of the incomes is skewed instead of being symmetric. A researcher states that because
In designing a new bed, you want the length of the bed to equal or exceed the height of at least 95% of all men. What is the minimum length of this bed?
The Wechsler test is used to measure IQ scores. It is designed so that the mean IQ score is 100 and the standard deviation is 15. It is known that IQ scores have a normal distribution. Assume that we want to find the probability that a randomly selected person has an IQ equal to 107. What is the
If selecting samples of size n = 2 from a population with a known mean and standard deviation, what requirement must be satisfied in order to assume that the distribution of the sample means is a normal distribution?
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
In each of the past 50 years, a simple random sample of 36 new movies is selected, and the mean of the 36 movie lengths (in minutes) is calculated. What is the approximate distribution of those sample means?
The standard casket has an inside length of 78 in.a. What percentage of men are too tall to fit in a standard casket, and what percentage of women are too tall to fit in a standard casket? Based on those results, does it appear that the standard casket size is adequate?b. A manufacturer of caskets
In a clinical trial of the allergy drug Nasonex, 2103 adult patients were treated with Nasonex and 14 of them developed viral infections.a. If two different adults are randomly selected from the treatment group, what is the probability that they both developed viral infections?b. Assuming that the
The Genetics & IVF Institute has developed methods for helping couples determine the gender of their children. For comparison, a large sample of randomly selected families with four children is obtained, and the proportion of girls in each family is recorded. Is the normal distribution a good
What does the notation μx̅ represent? What does the notation σx̅ represent?
What does the notation zα indicate?
Computers are often 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 5? Why or why not? What is the probability of getting a digit
a. What is a simple random sample?b. What is a voluntary response sample, and why is it generally unsuitable for statistical purposes?
In order to have a precision dance team with a uniform appearance, height restrictions are placed on the famous Rockette dancers at New York’s Radio City Music Hall. Because women have grown taller over the years, a more recent change now requires that a Rockette dancer must have a height between
The accompanying graph depicts the fuel consumption (in miles per gallon) for highway conditions of three cars. Does the graph depict the data fairly, or does it somehow distort the data? Explain. Highway Miles Per Gallon 20 Acura RL BMW 525i Saturn lon
Multiple choice test questions are commonly used for standardized tests, including the SAT, ACT, and LSAT. When scoring such questions, it is common to compensate for guessing. If a test consists of 100 multiple choice questions, each with possible answers of a, b, c, d, e, and each question has
a. If 1 SAT score is randomly selected, find the probability that it is less than 1500.b. If 100 SAT scores are randomly selected, find the probability that they have a mean less than 1500.
The normal quantile plot represents duration times (in seconds) of Old Faithful eruptions from Data Set 15 in Appendix B. Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. Data Set 15: Old Faithful Geyser Interval Interval
Greater than 124.0 voltsRefer to the continuous uniform distribution depicted in Figure 6-2. Assume that a voltage level between 123.0 volts and 125.0 volts is randomly selected, and find the probability that the given voltage level is selected.
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). 1 20
Probability of more than 8 Senators who are womenThe given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of “more than 20 defective items” corresponds to the area
a. If 1 SAT score is randomly selected, find the probability that it is greater than 1600.b. If 64 SAT scores are randomly selected, find the probability that they have a mean greater than 1600.
The normal quantile plot represents heights of women from Data Set 1 in Appendix B. Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. Data Set 1: Health Exam Results STATDISK: Data set name for males is Mhealth. AGE is
Less than 123.5 voltsRefer to the continuous uniform distribution depicted in Figure 6-2. Assume that a voltage level between 123.0 volts and 125.0 volts is randomly selected, and find the probability that the given voltage level is selected.
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). 80
Listed below are annual salaries (in thousands of dollars) for a simple random sample of NCAA Division 1-A head football coaches (based on data from the New York Times).235 159 492 530 138 125 128 900 360 212a. Find the mean x and express the
Assume that the following sample statistics were obtained from a simple random sample. Which of the following statements are true?a. The sample mean targets the population mean μ in the sense that the mean of all sample means is μ.b. The sample proportion targets the population proportion p in
Probability of at least 2 traffic tickets this yearThe given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of “more than 20 defective items” corresponds to the
Which of the following statistics are unbiased estimators of population parameters?a. Sample mean used to estimate a population meanb. Sample median used to estimate a population medianc. Sample proportion used to estimate a population proportiond. Sample variance used to estimate a population
a. If 1 SAT score is randomly selected, find the probability that it is between 1550 and 1575.b. If 25 SAT scores are randomly selected, find the probability that they have a mean between 1550 and 1575.c. Why can the central limit theorem be used in part (b), even though the sample size does not
The normal quantile plot represents weights (in pounds) of diet Coke from Data Set 17 in Appendix B. Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. Data Set 17: Weights and Volumes of Cola Weights are in pounds and
Between 123.2 volts and 124.7 voltsRefer to the continuous uniform distribution depicted in Figure 6-2. Assume that a voltage level between 123.0 volts and 125.0 volts is randomly selected, and find the probability that the given voltage level is selected.
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). 90 115
The serum cholesterol levels in men aged 18–24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7. Units are in mg/100 mL, and the data are based on the National Health Survey.a. If 1 man aged 18–24 is randomly selected, find the probability that his serum
Probability of fewer than 5 passengers who do not show up for a flightThe given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of “more than 20 defective items”
Samples of size n = 1000 are randomly selected from the population of the last digits of telephone numbers. If the sample mean is found for each sample, what is the distribution of the sample means?
a. If 1 SAT score is randomly selected, find the probability that it is between 1440 and 1480.b. If 16 SAT scores are randomly selected, find the probability that they have a mean between 1440 and 1480.c. Why can the central limit theorem be used in part (b), even though the sample size does not
The normal quantile plot represents the last two digits of telephone numbers of survey subjects. Examine the normal quantile plot and determine whether it depicts sample data from a population with a normal distribution. STATDISK 4.00 2.00 0.00 2.00 -4.00 20 40 60 80 100 X Value
Between 124.1 volts and 124.5 voltsRefer to the continuous uniform distribution depicted in Figure 6-2. Assume that a voltage level between 123.0 volts and 125.0 volts is randomly selected, and find the probability that the given voltage level is selected.
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). 75 110
Jennifer Jenson learns that the Newport Temp Agency has hired only 15 women among its last 40 new employees. She also learns that the pool of applicants is very large, with an equal number of qualified men and women. Find the probability that among 40 such applicants, the number of women is 15 or
Probability that the number of students who are absent is exactly 4The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of “more than 20 defective items”
Samples of size n = 1000 are randomly selected from the population of the last digits of telephone numbers, and the proportion of even numbers is found for each sample. What is the distribution of the sample proportions?
Based on data from the National Health and Nutrition Examination Survey, assume that weights of men are normally distributed with a mean of 172 lb and a standard deviation of 29 lb.a. Find the probability that if an individual man is randomly selected, his weight will be greater than 180 lb.b. Find
Using the systolic blood pressure levels and the elbow breadths of women, as listed in Data Set 1 in Appendix B, analyze each of the two data sets and determine whether each appears to come from a normally distributed population. Compare the results and give a possible explanation for any notable
The lengths (in hours) of flights of NASA?s Space Transport System (Shuttle) as listed in Data Set 10 in Appendix B. Refer to the indicated data set and determine whether the data have a normal distribution. Assume that this requirement is loose in the sense that the population distribution need
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z = 0.75
Find the indicated IQ score. 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). 06
a. Find the standard z score with a cumulative area to its left of 0.6700.b. Find the standard z score with a cumulative area to its right of 0.9960.c. Find the value of z0.025.
Probability of no more than 15 peas with green podsThe given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of “more than 20 defective items” corresponds to the
In Example 4, we assumed that samples of size are randomly selected without replacement from the population consisting of 2, 3, and 10, where the values are the numbers of people in households. Table 6-4 lists the nine different possible samples.a. Find the median of each of the nine samples, then
Cans of regular Pepsi are labeled to indicate that they contain 12 oz. Data Set 17 in Appendix B lists measured amounts for a sample of Pepsi cans. The sample statistics are n = 36 and x̅ = 12.29oz. If the Pepsi cans are filled so that μ = 12.00 oz (as labeled) and the population standard
Membership in Mensa requires an IQ score above 131.5. Nine candidates take IQ tests, and their summary results indicated that their mean IQ score is 133. (IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.)a. If 1 person is randomly selected from the general
The numbers of flights by NASA astronauts, as listed in Data Set 10 in Appendix B. Refer to the indicated data set and determine whether the data have a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z = -0.75
Find the indicated IQ score. 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). 0.8
A large number of simple random samples of size n = 85 are obtained from a large population of birth weights having a mean of 3420 g and a standard deviation of 495 g. The sample mean is calculated for each sample.a. What is the approximate shape of the distribution of the sample means?b. What is
Probability that the number of defective computer power supplies is between 12 and 16 inclusiveThe given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of “more than
Repeat Exercise 9 using standard deviations instead of medians.In Example 4, we assumed that samples of size are randomly selected without replacement from the population consisting of 2, 3, and 10, where the values are the numbers of people in households. Table 6-4 lists the nine different
A ski gondola in Vail, Colorado, carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 12 people or 2004 lb. That capacity will be exceeded if 12 people have weights with a mean greater than 2004/12 = 167 lb. Because men tend to weigh more than women, a
The values of heating degree days, as listed in Data Set 12 in Appendix B. Refer to the indicated data set and determine whether the data have a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it must be a
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 2 = -0.60 Łz = 1.20
Find the indicated IQ score. 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). 0.95
Under older Federal Aviation Administration rules, airlines had to estimate the weight of a passenger as 185 lb. (That amount is for an adult traveling in winter, and it includes 20 lb of carry-on baggage.) Current rules require an estimate of 195 lb. Men have weights that are normally distributed
Probability that the number of job applicants late for interviews is between 5 and 9 inclusiveThe given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of “more than
Repeat Exercise 9 using variances instead of medians.In Example 4, we assumed that samples of size are randomly selected without replacement from the population consisting of 2, 3, and 10, where the values are the numbers of people in households. Table 6-4 lists the nine different possible
The measured voltage levels from a generator, as listed in Data Set 13 in Appendix B. Refer to the indicated data set and determine whether the data have a normal distribution. Assume that this requirement is loose in the sense that the population distribution need not be exactly normal, but it
Less than - 1.50Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find the probability of each reading. (The given values are in Celsius degrees.) If
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. z = -0.90 z = 1.60 ||
Find the indicated IQ score. 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). 0.99
Listed below are the weights (in grams) of a simple random sample of United States one-dollar coins (from Data Set 20 in Appendix B). Do those weights appear to come from a population that has a normal distribution? Why or why not? Data Set 20: Coin Weights (grams) The "pre-1983 pennies" were made
Probability that exactly 24 felony indictments result in convictionsThe given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. For example, the probability of “more than 20 defective items”
Repeat Exercise 9 using means instead of medians.In Example 4, we assumed that samples of size are randomly selected without replacement from the population consisting of 2, 3, and 10, where the values are the numbers of people in households. Table 6-4 lists the nine different possible samples.a.
For women aged 18–24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on data from the National Health Survey). Hypertension is commonly defined as a systolic blood pressure above 140.a. If a woman between the ages of 18
Find the probability that a randomly selected adult has an IQ that is less than 115.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).
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 0.9798
In Example 1 it was noted that the author was mailed a survey from Viking River Cruises, and it included a request for an e-mail address. As in Example 1, assume that the survey was sent to 40,000 people and that for such surveys, the percentage of responses with an e-mail address is 3%. If the
With n = 10 and p = 0.5, find P (3). Do the following: (a) Find the indicated binomial probability by using Table A-1 in Appendix A. (b) If np ? 5 and nq ? 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np .01 .05
Find the probability that a randomly selected adult has an IQ greater than 131.5 (the requirement for membership in the Mensa organization).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).
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 0.2546
With n = 12 and p = 0.8, find P (9).Do the following: (a) Find the indicated binomial probability by using Table A-1 in Appendix A. (b) If np ≥ 5 and nq ≥ 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np < 5
Repeat Exercise 13 using medians instead of means.The ages (years) of the four U.S. presidents when they were assassinated in office are 56 (Lincoln), 49 (Garfield), 58 (McKinley), and 46 (Kennedy).a. Assuming that 2 of the ages are randomly selected with replacement, list the 16 different possible
The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.0 in. and a standard deviation of 2.8 in.a. If a male passenger is randomly selected, find the probability that he can fit through the doorway
Find the probability that a randomly selected adult has an IQ between 90 and 110 (referred to as the normal range).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).
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. 0.1075
With n = 8 and p = 0.9, find P (at least 6).Do the following: (a) Find the indicated binomial probability by using Table A-1 in Appendix A. (b) If np ≥ 5 and nq ≥ 5, also estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np
Repeat Exercise 13 using ranges instead of means.The ages (years) of the four U.S. presidents when they were assassinated in office are 56 (Lincoln), 49 (Garfield), 58 (McKinley), and 46 (Kennedy).a. Assuming that 2 of the ages are randomly selected with replacement, list the 16 different possible
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