Introductory Statistics 9th Edition Prem S. Mann - Solutions

According to the American Time Use Survey results released by the Bureau of Labor Statistics on June 24, 2015, on a typical day, 65% of American men age 15 and over spent some time doing household activities such as housework, cooking, lawn care, or financial and other household management. Assume
The package of Ecosmart Led 75-watt replacement bulbs that use only 14 watts claims that these bulbs have an average life of 24,966 hours. Assume that the lives of all such bulbs have an approximate normal distribution with a mean of 24,966 hours and a standard deviation of 2000 hours. Let x be the
In a January 2014 survey conducted by the Associated Press- We TV, 68% of American adults said that owning a home is the most important thing or a very important but not the most important thing (opportunityagenda.org). Assume that this percentage is true for the current population of American
According to a Gallup poll conducted April 3–6, 2014, 21% of Americans aged 18 to 29 said that college loans and/or expenses were the top financial problem facing their families. Assume that this percentage is true for the current population of Americans aged 18 to 29. Let p̂ be the proportion
According to a Gallup poll conducted January 5–8, 2014, 67% of American adults were dissatisfied with the way income and wealth are distributed in America. Assume that this percentage is true for the current population of American adults. Let p̂ be the proportion in a random sample of 400
According to the central limit theorem, the sampling distribution of p̂ is approximately normal when the sample is large. What is considered a large sample in the case of the proportion? Briefly explain.
How does the value of σp̂ change as the sample size increases? Explain. Assume n∕N ≤ .05.
What is the estimator of the population proportion? Is this estimator an unbiased estimator of p? Explain why or why not.
For a population, N = 2800 and p = .29. A random sample of 80 elements selected from this population gave p̂ = .33. Find the sampling error.
For a population, N = 12,000 and p = .71. A random sample of 900 elements selected from this population gave p̂ = .66. Find the sampling error.
Let p̂ be the proportion of elements in a sample that possess a characteristic.a. What is the mean of p̂ ?b. What is the formula to calculate the standard deviation of p̂ ?Assume n∕N ≤ .05.c. What condition(s) must hold true for the sampling distribution of p̂ to be approximately normal?
In a population of 18,700 subjects, 30% possess a certain characteristic. In a sample of 250 subjects selected from this population, 25% possess the same characteristic. How many subjects in the population and sample, respectively, possess this characteristic?
In a population of 5000 subjects, 600 possess a certain characteristic. In a sample of 120 subjects selected from this population, 18 possess the same characteristic. What are the values of the population and sample proportions?
In a population of 1000 subjects, 640 possess a certain characteristic. In a sample of 40 subjects selected from this population, 24 possess the same characteristic. What are the values of the population and sample proportions?
According to nerdwallet.com, the average household mortgage debt was $156,333 in August 2015. Suppose that the current distribution of mortgage debts of all U.S. households has a mean of $156,333 and a standard deviation of $36,000. Find the probability that the current average mortgage debt of a
According to the American Time Use Survey results released by the Bureau of Labor Statistics on June 24, 2015, Americans age 15 and over watched television for an average of 168 minutes per day. Suppose that the current distribution of times spent watching television per day by all Americans age 15
According to a Bureau of Labor Statistics release of March 25, 2015, financial analysts earn an average of $110,510 a year. Suppose that the current annual earnings of all financial analysts have the mean and standard deviation of $110,510 and $30,000, respectively. Find the probability that the
According to the American Time Use Survey results released by the Bureau of Labor Statistics on June 24, 2015, Americans age 15 and over watched television for an average of 168 minutes per day. Suppose that the current distribution of times spent watching television per day by all Americans age 15
According to the National Association of Colleges and Employers Spring 2015 Salary Survey, the average starting salary for 2014 college graduates was $48,127. Suppose that the mean starting salary of all 2014 college graduates was $48,127 with a standard deviation of $9200, and that this
A population has a normal distribution. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases.a. n = 94 b. n = 11
A population has a distribution that is skewed to the right. A sample of size n is selected from this population. Describe the shape of the sampling distribution of the sample mean for each of the following cases.a. n = 25 b. n = 80 c. n = 29
A population has a distribution that is skewed to the left. Indicate in which of the following cases the central limit theorem will apply to describe the sampling distribution of the sample mean.a. n = 400 b. n = 25 c. n = 36
What condition or conditions must hold true for the sampling distribution of the sample mean to be normal when the sample size is less than 30?
The standard deviation of the 2014 gross sales of all corporations is known to be $16.06 billion. Let x̅ be the mean of the 2014 gross sales of a sample of corporations. What sample size will produce the standard deviation of x̅ equal to $2.15 billion? Assume n∕N ≤ .05.
According to the 2015 Physician Compensation Report by Medscape (a subsidiary of WebMD), American orthopedists earned an average of $421,000 in 2014. Suppose that the mean and standard deviation of the 2014 earnings of all American orthopedists are $421,000 and $90,000, respectively. Let x̅ be the
How does the value of σx̅ change as the sample size increases? Explain.
According to a survey, 15% of U.S. adults with online services currently read e-books. Assume that this percentage is true for the current population of U.S. adults with online services. Find the probability that in a random sample of 600 U.S. adults with online services, the number who read
Under what conditions is the normal distribution usually used as an approximation to the binomial distribution?
A study has shown that 20% of all college textbooks have a price of $250 or higher. It is known that the standard deviation of the prices of all college textbooks is $50. Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?
The average monthly mortgage payment for all homeowners in a city is $2850. Suppose that the distribution of monthly mortgages paid by homeowners in this city follow an approximate normal distribution with a mean of $2850 and a standard deviation of $420. Find the probability that the monthly
One of the cars sold by Walt’s car dealership is a very popular subcompact car called the Rhino. The final sale price of the basic model of this car varies from customer to customer depending on the negotiating skills and persistence of the customer. Assume that these sale prices of this car are
Do the width and/or height of a normal distribution change when its standard deviation remains the same but its mean increases?
How do the width and height of a normal distribution change when its mean remains the same but its standard deviation decreases?
For a continuous probability distribution, explain why the following holds true. P(a < x < b) = P (a < x ≤ b) = P(a ≤ x < b) = P(a ≤ x ≤ b)
Let x be a continuous random variable. What is the probability that x assumes a single value, such as a?
The parameter/parameters of the Poisson probability distribution is/area. λ b. λ and x c. λ and e
What name is given to a table that lists all of the values that a discrete random variable x can assume and their corresponding probabilities?
What is the parameter of the Poisson probability distribution, and what does it mean?
During the 2014 NFL regular season, kickers converted 88% of the field goals attempted. Assume that this percentage is true for all kickers in the upcoming NFL season. Find the probability that a randomly selected kicker who will try 4 field goal attempts in a game willa. Convert all 4 field goal
According to a survey, 18% of the car owners said that they get the maintenance service done on their cars according to the schedule recommended by the auto company. Suppose that this result is true for the current population of car owners.a. Let x be a binomial random variable that denotes the
According to a survey, 70% of households said that they have never purchased organic fruits or vegetables. Suppose that this result is true for the current population of households.a. Let x be a binomial random variable that denotes the number of households in a random sample of 10 who have never
In a group of 12 persons, 3 are left-handed. Let x denote the number of left-handed persons in 2 randomly selected persons from these 12 persons. The following table lists the probability distribution of x. (Because of rounding, probabilities add to 1.0001.)Calculate the mean and standard deviation
One of the most profitable items at A1 Auto Security Shop is the remote starting system. The following table lists the probability distribution of x, where x represents the number of such systems installed on a given day at this shop and P(x) is the corresponding probability. Find the mean and
A limousine has eight tires on it. A fleet of such limos was fit with a batch of tires that mistakenly passed quality testing. The following table lists the probability distribution of the number of defective tires on this fleet of limos where x represents the number of defective tires on a limo
According to a survey, 35% of employees working at a very large company are happy with their jobs. Suppose that two employees are selected at random from this company. Let x denote the number of employees in this sample of two who are happy with their jobs.Construct the probability distribution
In a group of households, the national news is watched on one of the following three networks—ABC, CBS, or NBC. On a certain day, five households from this group randomly and independently decide which of these channels to watch. Let x be the number of households among these five that decide to
A couple is planning their wedding reception. The bride’s parents have given them a choice of four reception facilities, three caterers, five DJs, and two limo services. If the couple randomly selects one reception facility, one caterer, one DJ, and one limo service, how many different outcomes
A restaurant menu has four kinds of soups, eight kinds of main courses, five kinds of desserts, and six kinds of drinks. If a customer randomly selects one item from each of these four categories, how many different outcomes are possible?
A small ice cream shop has 10 flavors of ice cream and 5 kinds of toppings for its sundaes. How many different selections of one flavor of ice cream and one kind of topping are possible?
How many different outcomes are possible for 10 tosses of a coin?
How many different outcomes are possible for four rolls of a die?
According to the Gallup-Health ways Well-Being Index Survey conducted January 2–December 20, 2014, 35.2% of the adults are overweight and 27.7% are obese. What is the probability that a randomly selected adult is overweight or obese? Explain why this probability is not 1.0.
Jason and Lisa are planning an outdoor reception following their wedding. They estimate that the probability of bad weather is .25, that of a disruptive incident (a fight breaks out, the limousine is late, etc.) is .15, and that bad weather and a disruptive incident will occur is .08. Assuming
Six hundred adults were asked whether or not they watch for calories and fat content when they buy groceries. The following table gives the two-way classification of their responses, where yes means that an adult watches for calories and fat content and no means he/she does not watch.If one adult
How is the addition rule of probability for two mutually exclusive events different from the rule for two events that are not mutually exclusive?
In a survey of adults, 40% hold the opinion that there will be another housing bubble in the next four to six years. Three adults are selected at random.a. What is the probability that all three adults hold the opinion that there will be another housing bubble in the next four to six years?b. What
A company is to hire two new employees. They have prepared a final list of eight candidates, all of whom are equally qualified. Of these eight candidates, five are women. If the company decides to select two persons randomly from these eight candidates, what is the probability that both of them are
Seven hundred adults who eat ice cream regularly were asked about their favorite ice cream. The following table gives the two-way classification of their responses.a. One adult is randomly selected from these 700 adults. Find the following probabilities.i. P(man and vanilla)ii. P(other and woman)b.
Given that A and B are two independent events, find their joint probability for the following.a. P(A) = .29 and P(B) = .65b. P(A) = .03 and P(B) = .28
The probability that a randomly selected college student attended at least one major league baseball game last year is .12. What is the complementary event? What is the probability of this complementary event?
In a survey, 500 randomly selected adults who drink coffee were asked whether they usually drink coffee with or without sugar. Of these 500 adults, 290 are men and 200 drink coffee without sugar. Of the 200 who drink coffee without sugar, 130 are men. Are the events man and drinking coffee without
Six hundred adults were asked whether or not they watch for calories and fat content when they buy groceries. The following table gives the two-way classification of their responses, where yes means that an adult watches for calories and fat content and no means he/she does not watch.a. If one
Seven hundred adults who eat ice cream regularly were asked about their favorite ice cream. The following table gives the two-way classification of their responses.a. If one adult is randomly selected from these 700 adults, find the probability that this adulti. Likes chocolate ice creamii. Is a
What is meant by two mutually exclusive events? Give one example of two mutually exclusive events and another example of two events that are not mutually exclusive.
Suppose you want to find the (approximate) probability that a randomly selected family from Los Angeles earns more than $175,000 a year. How would you find this probability? What procedure would you use? Explain briefly.
In a sample of 500 families, 50 have a yearly income of less than $40,000, 180 have a yearly income of $40,000 to $80,000, and the remaining families have a yearly income of more than $80,000. Write the frequency distribution table for this problem. Calculate the relative frequencies for all
In a sample of 300 adults, 123 like chocolate ice cream and 84 like vanilla ice cream. One adult is randomly selected from these adults.a. What is the probability that this adult likes chocolate ice cream?b. What is the probability that this adult likes vanilla ice cream?Do these two probabilities
Jane and Mike are planning to go on a two-week vacation next summer. They have selected six vacation resorts, two of which are in Canada and remaining four are in Caribbean countries. Jane prefers going to a Canadian resort, and Mike prefers to vacation in one of the Caribbean countries. After much
In a group of 50 car owners, 8 own hybrid cars. If one car owner is selected at random from this group, what is the probability that this car owner owns a hybrid car?
A random sample of 2000 adults showed that 1320 of them have shopped at least once on the Internet. What is the (approximate) probability that a randomly selected adult has shopped on the Internet?
A hat contains 40 marbles. Of them, 18 are red and 22 are green. If one marble is randomly selected out of this hat, what is the probability that this marble isa. Red? b. Green?
A financial expert believes that the probability is .13 that the stock price of a specific technology company will double over the next year. Is this a case of classical, relative frequency, or subjective probability? Explain why.
The president of a company has a hunch that there is a .80 probability that the company will be successful in marketing a new brand of ice cream. Is this a case of classical, relative frequency, or subjective probability? Explain why.
An economist says that the probability is .47 that a randomly selected adult is in favor of keeping the Social Security system as it is, .32 that this adult is in favor of totally abolishing the Social Security system, and .21 that this adult does not have any opinion or is in favor of other
Which of the following values cannot be the probability of an event and why?2.4 3/8 −.63 .55 9/4 −2/9 1.0
Briefly explain for what kind of experiments we use the classical approach to calculate probabilities of events and for what kind of experiments we use the relative frequency approach.
A box contains three items that are labeled A, B, and C. Two items are selected at random (without replacement) from this box. List all the possible outcomes for this experiment. Write the sample space.
The following data give the number of hours worked last week by 18 randomly selected managers working for various Wall Street financial companies.45 54 63 79 48 50 49 52 7461
A company makes five different models of refrigerators. Last year they sold 16,652 refrigerators of all five models. The following table lists the number of different models of refrigerators sold last year and the prices for which they were sold.Calculate the weighted mean that represents the
Twenty randomly selected persons were asked to keep record of the number of times they used their debit cards during October 2015.The following data show their responses. 5 32 41 14
The following table shows the total population and the number of deaths (in thousands) due to heart attack for two age groups (in years) in Countries A and B for 2015.a. Calculate the death rate due to heart attack per 1000 population for the 30 years and under age group for each of the two
A survey of young people’s shopping habits in a small city during the summer months of 2015 showed the following: Shoppers aged 12 to 14 years took an average of 8 shopping trips per month and spent an average of $14 per trip. Shoppers aged 15 to 17 years took an average of 11 trips per month and
The following data give the odometer mileage (rounded to the nearest thousand miles) for all 20 cars that are for sale at a dealership.a. Calculate the values of the three quartiles and the interquartile range. Where does the number 77 fall in relation to these quartiles?b. Find the approximate
The following data give the odometer mileage (rounded to the nearest thousand miles) for all 20 cars that are for sale at a dealership.a. Calculate the values of the three quartiles and the interquartile range. Where does the number 77 fall in relation to these quartiles?b. Find the approximate
The following table gives the distribution of the amounts of rainfall (in inches) for July 2015 for 50 cities.Rainfall Number of Cities0 to less
A company makes five different models of cameras. Last month they sold 13,884 cameras of all five models. The following table lists the number of different models of cameras sold during the last month and the prices for which they were sold.Calculate the weighted mean that represents the average
An electronics store sold 4828 televisions last year. The following table lists the number of different models of televisions sold and the prices for which they were sold.Calculate the weighted mean that represents the average price for which these 4828 televisions were sold. Price Television
The following data give the odometer mileage (rounded to the nearest thousand miles) for all 20 cars that are for sale at a dealership.a. Calculate the mean and median. Do these data have a mode? Why or why not?b. Calculate the 10% trimmed mean for these data.c. Compute the range, variance,
The following data give the number of patients who visited a walk-in clinic on each of 24 randomly selected days.Prepare a box-and-whisker plot. Comment on the skewness of these data. 23 37 26 19 33 22 30 42 24 26 64 28 32 37 29 38 24 35 20 34 38 28 16
The following data give the annual salaries (in thousand dollars) of 20 randomly selected health care workers.Prepare a box-and-whisker plot. Are these dataThe following data give the number of patients who visited awalk-in clinic on each of 24 randomly selected days. skewed in any direction? 71 57
The following data give the total food expenditures (in dollars) for the past one month for a sample of 20 families.Prepare a box-and-whisker plot. Is the distribution of these data symmetric or skewed? Are there any outliers? If so, classify them as mild or extreme. 1125 530 1234 595 427 872 1480
The following data give the 2015 bonuses (in thousands of dollars) of 15 randomly selected Wall Street managers.Prepare a box-and-whisker plot. Are these data skewed in any direction? 107 61 89 208 53 258 122 175 136 361 247 67 781 391 71
Briefly explain what summary measures are used to construct a box-and-whisker plot.
The following data give the annual salaries (in thousand dollars) of 20 randomly selected health care workers.a. Calculate the values of the three quartiles and the interquartile range. Where does the value 57 fall in relation to these quartiles?b. Find the approximate value of the 30th percentile.
The following data give the total food expenditures (in dollars) for the past one month for a sample of 20 families.a. Calculate the values of the three quartiles and the interquartile range.b. Find the approximate value of the 57th percentile.c. Calculate the percentile rank of 1046. Give a brief
The one-way commuting times from home to work for all employees working at a large company have a bell-shaped curve with a mean of 34 minutes and a standard deviation of 8 minutes. Using the empirical rule, find the approximate percentages of the employees at this company who have one-way commuting
The one-way commuting times from home to work for all employees working at a large company have a mean of 34 minutes and a standard deviation of 8 minutes.a. Using Chebyshev’s theorem, find the minimum percentage of employees at this company who have one-way commuting times in the following
The following data give the amounts (in dollars) spent last month on food by 400 randomly selected families.Food Expenditure
The following table gives information on the amounts (in dollars) of electric bills for August 2015 for a sample of 50 families.Amount of Electric Bill
The following data give the 2015 bonuses (in thousands of dollars) of 10 randomly selected Wall Street managers.127 82 45 99 153 3261 77 108 68 278a. Calculate the range, variance,

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Introductory Statistics 9th Edition Prem S. Mann - Solutions

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