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mathematics
statistics

Elementary Statistics A Step By Step Approach 8th Edition Allan Bluman - Solutions

Another measure of average is called the midquartile; it is the numerical value halfway between Q1 and Q3, and the formula isUsing this formula and other formulas, find Q1, Q2, Q3, the midquartile, and the interquartile range for each data set.a. 5, 12, 16, 25, 32, 38 b. 53, 62, 78, 94, 96, 99, 103
If the average number of vacation days for a selection of various countries has a mean of 29.4 days and a standard deviation of 8.6, find the z scores for the average number of vacation days in each of these countries.Canada 26 daysItaly 42 daysUnited States 13 days
8, 12, 32, 6, 27, 19, 54 Identify the five-number summary and find the interquartile range.
Identify the maximum value, minimum value, median, first quartile, third quartile, and interquartile range.
Construct a boxplot for the following data and comment on the shape of the distribution representing the number of games pitched by major league baseball’s earned run average (ERA) leaders for the past few years. 30 34 29 30 34 29 31 33 34 27 30 27 34 32
Construct a boxplot for the following data which represent the number of innings pitched by the ERA leaders for the past few years. Comment on the shape of the distribution. 192 228 186 199 238 217 213 234 264 187 214 115 238 246
The number of teacher strikes over a 13-year period in Pennsylvania is shown. Construct a boxplot for the data. Is the distribution symmetric?
Construct a boxplot for the number (in millions) of visitors who traveled to a foreign country each year for a random selection of years. Comment on the skewness of the distribution. 4.3 0.5 0.6 0.8 0.5 0.4 3.8 1.3 0.4 0.3
Construct a boxplot and comment on its skewness for the number of tornadoes recorded each month in 2005. 33 10 62 132 123 316 138 123 133 18 150 26
These data represent the volumes in cubic yards of the largest dams in the United States and in South America. Construct a boxplot of the data for each region and compare the distributions.United States ......South
A four-month record for the number of tornadoes in 2003€“2005 is given here.a. Which month had the highest mean number of tornadoes for this 3-year period? b. Which year has the highest mean number of tornadoes for this 4-month period? c. Construct three boxplots and compare the distributions.
A modified boxplot can be drawn by placing a box around Q1 and Q3 and then extending the whiskers to the largest and/or smallest values within 1.5 times the interquartile range (that is, Q3 €“ Q1). Mild outliers are values between 1.5(IQR) and 3(IQR). Extreme outliers are data values
19, 16, 48, 22, 7 Identify the five-number summary and find the interquartile range.
362, 589, 437, 316, 192, 188 Identify the five-number summary and find the interquartile range.
147, 243, 156, 632, 543, 303 Identify the five-number summary and find the interquartile range.
14.6, 19.8, 16.3, 15.5, 18.2 Identify the five-number summary and find the interquartile range.
9.7, 4.6, 2.2, 3.7, 6.2, 9.4, 3.8 Identify the five-number summary and find the interquartile range.
Identify the maximum value, minimum value, median, first quartile, third quartile, and interquartile range.
Identify the maximum value, minimum value, median, first quartile, third quartile, and interquartile range.
Identify the maximum value, minimum value, median, first quartile, third quartile, and interquartile range.
The net worth (in billions of dollars) of a sample of the richest people in the United States is shown. Find the mean, median, mode, midrange, variance, and standard deviation for the data.59 52 28 26 1919 18 17 17 17
If the average number of textbooks in professors’ offices is 16, the standard deviation is 5, and the average age of the professors is 43, with a standard deviation of 8, which data set is more variable?
A survey of bookstores showed that the average number of magazines carried is 56, with a standard deviation of 12. The same survey showed that the average length of time each store had been in business was 6 years, with a standard deviation of 2.5 years. Which is more variable, the number of
The number of years served by selected past members of the U.S. Supreme Court is listed below.Find the percentile rank for each value. Which value corresponds to the 40th percentile? Construct a boxplot for the data and comment on their shape.19, 15, 16, 24, 17, 4, 3, 31, 23, 5, 33
The salaries (in millions of dollars) for 29 NFL teams for the 1999–2000 season are given in this frequency distribution.Class limits Frequency39.9–42.8.....242.9–45.8.....245.9–48.8.....548.9–51.8.....551.9–54.8.....124.9–57.8 ......3a. Construct a percentile graph.b. Find the values
Check each data set for outliers.a. 506, 511, 517, 514, 400, 521 b. 3, 7, 9, 6, 8, 10, 14, 16, 20, 12c. 14, 18, 27, 26, 19, 13, 5, 25 d. 112, 157, 192, 116, 153, 129, 131
A survey of car rental agencies shows that the average cost of a car rental is $0.32 per mile. The standard deviation is $0.03. Using Chebyshev’s theorem, find the range in which at least 75% of the data values will fall.
The average earnings of year-round full-time workers 25–34 years old with a bachelor’s degree or higher were $58,500 in 2003. If the standard deviation is $11,200, what can you say about the percentage of these workers who earn (3–2)a. Between $47,300 and $69,700? b. More than $80,900? c. How
The average labor charge for automobile mechanics is $54 per hour. The standard deviation is $4. Find the minimum percentage of data values that will fall within the range of $48 to $60. Use Chebyshev’s theorem.
For a certain type of job, it costs a company an average of $231 to train an employee to perform the task. The standard deviation is $5. Find the minimum percentage of data values that will fall in the range of $219 to $243. Use Chebyshev’s theorem.
The average delivery charge for a refrigerator is $32. The standard deviation is $4. Find the minimum percentage of data values that will fall in the range of $20 to $44. Use Chebyshev’s theorem.
The number of shark attacks and deaths over a recent 5-year period is shown. Find the mean, median, mode, midrange, variance, and standard deviation for the data. Which data set is more variable?
Which of these exam grades has a better relative position? (3–3)a. A grade of 82 on a test with = 85 and s = 6 – 0.5b. A grade of 56 on a test with = 60 and s 5– 0.8
The number of sites at which the top nine movies (based on the daily gross earnings) opened in a particular week is indicated below. 3017 3687 2525 2516 2820 2579 3211 3044 2330 Construct a boxplot for the data. The 10th movie on the list opened at only 909 theaters. Add this number to the
The data shown here represent the number of hours that 12 part-time employees at a toy store worked during the weeks before and after Christmas. Construct two boxplots and compare the distributions.
The mean of the times it takes a commuter to get to work in Baltimore is 29.7 minutes. If the standard deviation is 6 minutes, within what limits would you expect approximately 68% of the times to fall? Assume the distribution is approximately bell shaped.
Twelve batteries were tested to see how many hours they would last. The frequency distribution is shown here.Hours Frequency1–3 ......14–6 ......47–9 ......510–12 .....113–15 .....1a. Meanb. Modal class c. Varianced. Standard deviation
The mean SAT math scores for selected states are represented below. Find the mean class, modal class, variance, and standard deviation, and comment on the shape of the data.Score Frequency478–504 ...... 4505–531 ......
Shown here is a frequency distribution for the rise in tides at 30 selected locations in the United States.Rise in tides (inches) Frequency12.5–27.5 ..........627.5–42.5 ..........342.5–57.5 ..........557.5–72.5 ..........872.5–87.5 ..........687.5–102.5 ...........2a. Meanb. Modal
The fuel capacity in gallons of 50 randomly selected cars is shown here.Class Frequency10–12 .......613–15 .......416–18 .......1419–21 .......1522–24 .......825–27 .......228–30 .......1 50Find each of these.a. Mean b. Modal class c. Variance d. Standard deviation
A survey showed the number of viewers and number of households of four television networks. Find the average number of viewers, using the weighted mean.
An investor calculated these percentages of each of three stock investments with payoffs as shown. Find the average payoff. Use the weighted mean.
In an advertisement, a transmission service center stated that the average years of service of its employees were 13. The distribution is shown here. Using the weighted mean, calculate the correct average. Number of employees Years of service 8...........3 1...........6 1...........30
Classify each statement as an example of classical probability, empirical probability, or subjective probability.a. The probability that a person will watch the 6 o’clock evening news is 0.15. b. The probability of winning at a Chuck-a-Luck game is . c. The probability that a bus will be in an
If a die is rolled one time, find these probabilities.a. Getting a 2b. Getting a number greater than 6 c. Getting an odd numberd. Getting a 4 or an odd numbere. Getting a number less than 7 f. Getting a number greater than or equal to g. Getting a number greater than 2 and an even number
If two dice are rolled one time, find the probability of getting these results.a. A sum of 9b. A sum of 7 or 11c. Doublesd. A sum less than 9e. A sum greater than or equal to 10
If one card is drawn from a deck, find the probability of getting these results.a. A queenb. A clubc. A queen of clubsd. A 3 or an 8e. A 6 or a spadef. A 6 and a spadeg. A black kingh. A red card and a 7i. A diamond or a heartj. A black card
A shopping mall has set up a promotion as follows. With any mall purchase of $50 or more, the customer gets to spin the wheel shown here. If a number 1 comes up, the customer wins $10. If the number 2 comes up, the customer wins $5; and if the number 3 or 4 comes up, the customer wins a discount
Choose one of the 50 states at random.a. What is the probability that it begins with M?b. What is the probability that it doesn’t begin with a vowel?
Human blood is grouped into four types. The percentages of Americans with each type are listed below.O 43% A 40% B 12% AB 5%Choose one American at random. Find the probability that this persona. Has type O bloodb. Has type A or B c. Does not have type O or A
A prime number is a number that is evenly divisible only by 1 and itself. The prime numbers less than 100 are listed below.2 3 5 7 11 13 17 19 23 29 3137 41 43 47 53 59 61 67 71 73 7983 89 97Choose one of these numbers at random. Find the probability thata. The number is evenb. The sum of the
Rural speed limits for all 50 states are indicated below.Choose one state at random. Find the probability that its speed limit is a. 60 or 70 miles per hour b. Greater than 65 miles per hour c. 70 miles per hour or less
A couple has three children. Find each probability.a. All boysb. All girls or all boysc. Exactly two boys or two girlsd. At least one child of each gender
Elementary and secondary schools were classified by the number of computers they had. Choose one of these schools at random.Choose one school at random. Find the probability that it has a. 50 or fewer computers b. More than 100 computers c. No more than 20 computers
The following information shows the amount of debt students who graduated from college incur.If a person who graduates has some debt, find the probability that a. It is less than $5001 b. It is more than $20,000 c. It is between $1 and $20,000 d. It is more than $50,000
Of the top 10 cars and trucks based on gas mileage, 4 are Hondas, 3 are Toyotas, and 3 are Volkswagens. Choose one at random. Find the probability that it is a. Japanese b. Japanese or German c. Not foreign
A breakdown of the sources of energy used in the United States is shown below. Choose one energy source at random. Find the probability that it is a. Not oil 0.61 b. Natural gas or oil 0.63 c. Nuclear 0.08 Oil 39% Natural gas 24% Coal 23% Nuclear 8% Hydropower 3% Other 3%
Roll two dice and multiply the numbers.a. Write out the sample space002Eb. What is the probability that the product is a multiple of 6?c. What is the probability that the product is less than 10?
A box contains a $1 bill, a $5 bill, a $10 bill, and a $20 bill. A bill is selected at random, and it is not replaced; then a second bill is selected at random. Draw a tree diagram and determine the sample space.
A box contains a $1 bill, a $5 bill, a $10 bill, and a $20 bill. A bill is selected at random, and it is not replaced; then a second bill is selected at random. Draw a tree diagram and determine the sample space.
Draw a tree diagram and determine the sample space for tossing four coins.
Four balls numbered 1 through 4 are placed in a box. A ball is selected at random, and its number is noted; then it is replaced. A second ball is selected at random, and its number is noted. Draw a tree diagram and determine the sample space.
A family special at a neighborhood restaurant offers dinner for four for $39.99. There are 3 appetizers available, 4 entrees, and 3 desserts from which to choose. The special includes one of each. Represent the possible dinner combinations with a tree diagram.
First-year students at a particular college must take one English class, one class in mathematics, a first-year seminar, and an elective. There are 2 English classes to choose from, 3 mathematics classes, 5 electives, and everyone takes the same first-year seminar. Represent the possible schedules,
A coin is tossed; if it falls heads up, it is tossed again. If it falls tails up, a die is rolled. Draw a tree diagram and determine the outcomes.
The distribution of ages of CEOs is as follows: Age Frequency 21–30......1 31–40......8 41–50.....27 51–60.....29 61–70.....24 71–up.....11 If a CEO is selected at random, find the probability that his or her age is a. Between 31 and 40 b. Under 31 c. Over 30 and under 51 d. Under
The wheel spinner shown here is spun twice. Find the sample space, and then determine the probability of the following events.a. An odd number on the first spin and an even number on the second spin (Note: 0 is considered even.) b. A sum greater than 4 c. Even numbers on both spins d. A sum that is
Odds are used in gambling games to make them fair. For example, if you rolled a die and won every time you rolled a 6, then you would win on average once every 6 times. So that the game is fair, the odds of 5 to 1 are given. This means that if you bet $1 and won, you could win $5. On average, you
A single card is drawn from a deck. Find the probability of selecting the following. a. A 4 or a diamond b. A club or a diamond c. A jack or a black card
In a statistics class there are 18 juniors and 10 seniors; 6 of the seniors are females, and 12 of the juniors are males. If a student is selected at random, find the probability of selecting the following. a. A junior or a female b. A senior or a female c. A junior or a senior
At a used-book sale, 100 books are adult books and 160 are children’s books. Of the adult books, 70 are nonfiction while 60 of the children’s books are nonfiction. If a book is selected at random, find the probability that it is a. Fiction b. Not a children’s nonfiction book c. An adult
According to the Bureau of the Census, the following statistics describe the number (in thousands) of young adults living at home or in a dormitory in the year 2004.Choose one student at random. Find the probability that the student isa. A female student aged 25–34 0.058b. Male or aged 18–24
The chart below shows the numbers of endangered and threatened species both here in the United States and abroad.Choose one species at random. Find the probability that it is a. Threatened and in the United States 0.072 b. An endangered foreign bird 0.229 c. A mammal or a threatened foreign species
The number of multiple births in the United States for a recent year indicated that there were 128,665 sets of twins, 7110 sets of triplets, 468 sets of quadruplets, and 85 sets of quintuplets. Choose one set of siblings at random. Find the probability that it a. Represented more than two babies
In a recent year there were the following numbers (in thousands) of licensed drivers in the United States.Choose one driver at random. Find the probability that the driver is a. Male and 19 or under b. Age 20 or female c. At least 20 years old
In a recent survey, the following data were obtained in response to the question, €œIf thenumber of summer classes were increased, would you be more likely to enroll in one or more of them?€If a student is selected at random, find the probability that the student a. Has no
A local postal carrier distributes firstclass letters, advertisements, and magazines. For a certain day, she distributed the following numbers of each type of item.If an item of mail is selected at random, find these probabilities. a. The item went to a home. b. The item was an ad, or it went to a
The frequency distribution shown here illustrates the number of medical tests conducted on 30 randomly selected emergency patients. Number of tests Number of performed patients 0.......... 12 1 ............8 2 ............2 3 ............3 4 or more .......5 If a patient
Determine whether these events are mutually exclusive. a. Roll a die: Get an even number, and get a number less than 3. No b. Roll a die: Get a prime number (2, 3, 5), and get an odd number. No c. Roll a die: Get a number greater than 3, and get a number less than 3. Yes d. Select a student in
A social organization of 32 members sold college sweatshirts as a fundraiser. The results of their sale are shown below. No. of sweatshirts No. of students 0 ..............2 1–5 .............13 6–10 ............8 11–15 .............4 16–20 .............4 20+.............1 Choose one
A sales representative who visits customers at home finds she sells 0, 1, 2, 3, or 4 items according to the following frequency distribution. Items sold Frequency 0..........8 1 ............10 2 ..........3 3 ..........2 4 ..........1 1...........3 Find the probability that she sells the
A recent study of 300 patients found that of 100 alcoholic patients, 87 had elevated cholesterol levels, and of 200 nonalcoholic patients, 43 had elevated cholesterol levels. If a patient is selected at random, find the probability that the patient is the following. a. An alcoholic with elevated
Selecting a Card If one card is drawn from an ordinary deck of cards, find the probability of getting the following. a. A king or a queen or a jack b. A club or a heart or a spade c. A king or a queen or a diamond d. An ace or a diamond or a heart e. A 9 or a 10 or a spade or a club
Two dice are rolled. Find the probability of getting a. A sum of 8, 9, or 10 b. Doubles or a sum of 7 c. A sum greater than 9 or less than 4 d. Based on the answers to a, b, and c, which is least likely to occur?
Three dice are rolled. Find the probability of getting a. Triples b. A sum of
The table below represents the college degrees awarded in a recent academic year by gender.Choose a degree at random. Find the probability that it is a. A bachelor€™s degree b. A doctorate or a degree awarded to a woman c. A doctorate awarded to a woman d. Not a master€™s
A media rental store rented the following number of movie titles in each of these categories: 170 horror, 230 drama, 120 mystery, 310 romance, and 150 comedy. If a person selects a movie to rent, find the probability that it is a romance or a comedy. Is this event likely or unlikely to occur?
On a hospital staff, there are 4 dermatologists, 7 surgeons, 5 general practitioners, 3 psychiatrists, and 3 orthopedic specialists. If a doctor is selected at random, find the probability that the doctor is a. A psychiatrist, surgeon, or dermatologist b. A general practitioner or surgeon c. An
The probability that a given tourist goes to the amusement park is 0.47, and the probability that she goes to the water park is 0.58. If the probability that she goes to either the water park or the amusement park is 0.95, what is the probability that she visits both of the parks on vacation?
State which events are independent and which are dependent. a. Tossing a coin and drawing a card from a deck Independent b. Drawing a ball from an urn, not replacing it, and then drawing a second ball Dependent c. Getting a raise in salary and purchasing a new car Dependent d. Driving on ice and
If 2 cards are selected from a standard deck of 52 cards without replacement, find these probabilities. a. Both are spades. b. Both are the same suit. c. Both are kings.
In 2006, 86% of U.S. households had cable TV. Choose 3 households at random. Find the probability that a. None of the 3 households had cable TV b. All 3 households had cable TV c. At least 1 of the 3 households had cable TV
Four cards are drawn from a deck without replacement. Find these probabilities. a. All are kings. b. All are diamonds. c. All are red cards.
A manufacturer makes two models of an item: model I, which accounts for 80% of unit sales, and model II, which accounts for 20% of unit sales. Because of defects, the manufacturer has to replace (or exchange) 10% of its model I and 18% of its model II. If a model is selected at random, find the
In a recent year 8,073,000 male students and 10,980,000 female students were enrolled as undergraduates. Receiving aid were 60.6% of the male students and 65.2% of the female students. Of those receiving aid, 44.8% of the males got federal aid and 50.4% of the females got federal aid. Choose 1
An insurance company classifies drivers as low-risk, medium-risk, and highrisk. Of those insured, 60% are low-risk, 30% are medium-risk, and 10% are high-risk. After a study, the company finds that during a 1-year period, 1% of the low-risk drivers had an accident, 5% of the medium-risk drivers had
A production process produces an item. On average, 15% of all items produced are defective. Each item is inspected before being shipped, and the inspector misclassifies an item 10% of the time. What proportion of the items will be “classified as good”? What is the probability that an item is
Sixty-nine percent of U.S. heads of households play video or computer games. Choose 4 heads of households at random. Find the probability that a. None play video or computer games b. All four do
The Gift Basket Store had the following premade gift baskets containing the following combinations in stock.Choose 1 basket at random. Find the probability that it contains a. Coffee or candy 0.7143 b. Tea given that it contains mugs 0.4348 c. Tea and cookies 0.1558
In addition to being grouped into four types, human blood is grouped by its Rhesus (Rh) factor. Consider the figures below which show the distributions of these groups for Americans.Choose 1 American at random. Find the probability that the person a. Is a universal donor, i.e., has O negative blood

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