Statistics Final Exam
The probability that a football game will go into overtime is 10%. What is the probability that two of three football games will go to into overtime?
0.027
The probability that a house in an urban area will develop a leak is 3%. If 18 houses are randomly selected, what is the probability that none of the houses will develop a leak?
0.030
The grocery expenses for six families were $43.80, $66.14, $57.93, $81.44, $70.44, and $45.86 . Compute the mean grocery bill. Round your answer to the nearest cent.
$60.94
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 378 seconds.
0.0107
Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed. Suppose that it is reported in the news that 8% of the people living and working in Kokomo feel "very satisfied" with their commute time to work. What is the travel time to work that separates the bottom 8% of people with the shortest travel times and the upper 92%? Round to the nearest tenth of a minute.
10.7 minutes
The numbers listed below represent the amount of precipitation (in inches) last year in six different U.S. cities. 23.3 12.3 41.7 29.0 23.4 12.1
11.11 in.
Ten parents were asked the ages of their oldest child. The results are shown below. 29 12 10 6 22 19 16 14 2 28 What is the IQR for this set of data?
12
In a study of 1350 elementary school children, 118 out of the 615 girls in the study said they want to be a teacher when they grow up.What percent of girls want to be a teacher when they grow up?
19.2%
The probability is 0.1 that a person shopping at a certain store will spend less than $20. For groups of size 23, find the expected number of shoppers who spend less than $20.
2.3
Use the following information to answer the question. The distribution of the number of hours of sleep people get per night is unimodal and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours. Approximately what percent of people sleep between 6 and 7.5 hours per night?
34%
Use the following information to answer the question. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric. In 2002, actor Adrian Brody won an academy award in for the movie "The Pianist." He was 29-years-old. Finish the statement: "According to the Empirical Rule, the ages of nearly all lead actors will be between and years. Adrien Brody was this range when she won the academy award."
6.8; 66.0; within
In a certain town, 80 percent of voters are in favor of a given ballot measure and 20 percent are opposed. For groups of 340 voters, find the expected number of voters who oppose the measure.
68
At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5?
68%
Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). For what percentage of great lakes states would you expect the economic impact from fishing to be between $151.00 and $485.00 (in millions of dollars)?
95%
A large state university conducted a survey among their students and received 400 responses. The survey asked the students to provide the following information: *Age *Year in School (Freshman, Sophomore, Junior, Senior) *Major What type of graph would you use to describe the variable Major?
A bar chart because Major is a categorical variable.
Ticket sales per hour = -631.25 + 11.25(current temperature in °F) What is the predicted number of tickets sold per hour if the temperature is 86°F? Round to the nearest whole ticket.
About 336 tickets
Determine which of the following five variables are numerical and which are categorical. age, gender, height, favorite candy, eye color
Age and height are numerical variables. Gender, favorite candy, and eye color are categorical variables.
Determine which of the following five variables are numerical and which are categorical. age, gender, weight, ethnicity, favorite math class
Age and weight are numerical variables. Gender, ethnicity, and favorite math class are categorical variables.
Which of the following statements regarding the correlation coefficient is NOT true?
All of these statements are TRUE
What effects might an outlier have on a regression equation?
An outlier may affect both the slope and the correlation coefficient of a regression equation.
If 20 babies are born, how often are there 12 or more female babies? Assume that the gender of a baby is a random event. Which of the following experiments would not simulate this situation?
Flip a coin twenty times. Designate a head to mean "female" and a tail to mean "male." Roll a die twenty times. Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 to mean "male." Choose the first twenty digits from a row in the random number table. Designate odd numbers to mean "female" and even numbers to mean "male."
Which of the following statements is true about the "law of large numbers" (LLN)?
If you repeat a random experiment many, many times, your outcomes should on average approach the theoretical average.
Suppose that the probability that a person between the ages of 19 and 24 buys at least one tabloid magazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 were asked "Do you buy at least one tabloid magazine per week?", would you be surprised if 45 or more said yes to this question? Why?
No, 45 is within the expected range of people.
The graph below displays the number of applications for a concealed weapons permit in Montcalm County, Michigan, for each of three years. A reporter interprets this graph to mean that applications in 2010 are more than twice the level in 2008. Is the reporter making a correct interpretation?
No. Although the 2010 bar is more than twice the height of the 2008, the bars do not begin at 0 applications, so the graph does not correctly represent the data. Fifty-five is not equal to two times the number of applications made in 2008.
Determine which of the given procedures describe a binomial distribution.
Observing that ten out of the next twenty customers at a grocery store checkout use a credit card given that the probability of using a credit card is 0.58.
Suppose temperatures and monthly ice cream sales were measured for 100 randomly selected cities. Which variable is the explanatory variable and which one is the response?
Temperature is the explanatory variable and ice cream sales is the response because a city's temperature could explain the amount of ice cream sales.
Which of the following statements is true about the Law of Large Numbers (LLN)?
The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.
Consider the following statement, "Babies who breastfeed are less likely to grow into children with behavioral problems by the time they reach age 5 than those who receive formula milk." Which of the following is a plausible confounding variable in this study?
The age at which breastfeeding ends Mother's social-economic status The quality of the formula milk
Before opening a new dealership, an auto manufacturer wants to gather information about car ownership and driving habits of the local residents. The marketing manager of the company randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, she receives 85 back. What is the problem with how the information is gathered?
The only responses were from people who chose to send the survey back.
Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed. Which of these statements is asking for a probability?
What percentage of people living and working in Kokomo have a travel time to work that is between thirteen and fifteen minutes?
The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 70 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store.
number of items - discrete; total time - continuous
The number of parents who attended parent teacher conferences at a local elementary school is an example of what type of variable?
numerical variable
A gym is offering a new 6-week diet plan for its members. Members who sign up for the program are weighed and measured once a week for the duration of the program. The owners of the gym want to know if the diet plan actually helps people lose weight. What variable could be a possible confounding factor in determining the cause of weight loss?
the persons exercise routine
A bag contains 7 red marbles, 8 blue marbles, and 9 green marbles. Jeffery claims that if a marble is selected at random from the bag, the probability of choosing a blue marble is . Is this an example of empirical probability or theoretical probability?
theoretical
Obtain the five-number summary for the given data.1, 3, 6, 7, 9, 11, 14
1, 3, 7, 11, 14
The heights (in meters) of five adults are listed below. Calculate the mean height of these adults. 1.57, 1.65, 1.73, 1.75, 1.78
1.70 meters
The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 17. Find the standard deviation for the number of seeds germinating in each batch.
1.9
In a sample of 775 senior citizens, approximately 67% said that they had seen a television commercial for life insurance. About how many senior citizens is this?
519
The normal model N(58, 21) describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z-score of 1.78. What is the weight of this egg in grams? Round to the nearest hundredth of a gram.
95.38 grams
Which of the following are mutually exclusive events?
A car buyer chose "fuel efficiency" and "other" as their most important factor for their purchase.
The two histograms below display the exact same data. How do the plots differ?
Histogram (i) uses relative frequencies to show the proportion of observations at a given value. Histogram (ii) uses frequencies to simply count the number of observations at a given value.
Suppose we have a distribution of student exam scores on an easy test. What measure of spread would be best to describe this data?
The spread should be described with the IQR because the distribution will be skewed to the left.
Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars. Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration). The economic impact of fishing for nearly all great lakes states should fall within what range (in millions of dollars)?
$67.5 to $568.5
In a recent poll of 1200 randomly selected adult office workers, 32% said they had worn a Halloween costume to the office at least once. What is the standard error for the estimate of the proportion of all American adult office workers that have worn a Halloween costume to the office? Round to the nearest ten-thousandth.
0.0135
The probability that an individual has 20-20 vision is 0.14. In a class of 77 students, what is the probability of finding five people with 20-20 vision?
0.020
Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel. What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.
0.025
An airline estimates that 94% of people booked on their flights actually show up. If the airline books 73 people on a flight for which the maximum number is 71, what is the probability that the number of people who show up will exceed the capacity of the plane?
0.062
In a recent survey, 72% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 10 of them favor the building of the health center.
0.230
Which of the following would likely show a bimodal distribution in a histogram?
The heights of all students in a high school band.
Marital status of each member of a randomly selected group of adults is an example of what type of variable?
categorical variable
Suppose that a recent poll of American households about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually exclusive.What is the probability that all three randomly selected households own a dog? (Round to the nearest hundredth)
0.09
A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr. Roughly what proportion of cars are driving between 60 and 70 mi/hr? Round to the nearest thousandth)
0.157
The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.12 ounces and a standard deviation of 0.08 ounce. The cans only hold 12.20 ounces of soda. Every can that has more than 12.20 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process?
0.1587
Suppose that a recent poll of American households about car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports car. Suppose that three households are selected randomly and with replacement. What is the probability that at least one of the three randomly selected households own a sports car? (Round to the nearest thousandth)
0.200
Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket. What is the probability that exactly seven out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth.
0.264
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 IQ score separating the top 16% from the others.
114.9
The table gives the GPA and gender of students in a business class.Is the format of the data set stacked or unstacked?
stacked
Is the following an example of theoretical probability or empirical probability? A card player declares that there is a one in thirteen chance that the next card pulled from a well-shuffled, full deck will be a queen.
theoretical
Is the following an example of theoretical probability or empirical probability? At a carnival shell game the player can pay three dollars and choose the shell that he or she believes is hiding the prize. There are four shells that are thoroughly mixed up after each guess. The player concludes that there is a one in four chance of randomly picking the winning shell.
theoretical
The table gives the GPA of some students in two math classes. One class meets in the morning and one in the afternoon. Is the format of the data set stacked or unstacked?
unstacked
The following nine values represent race finish times in hours for a randomly selected group of participants in an extreme 10k race (a 10k race with obstacles). Which of the following is closest to the mean of the following data set? 1.0, 1.2, 1.2, 1.3, 1.4, 1.5, 1.5, 1.7, 2.1
x is about 1.4 hours
The age distribution of students at a community college is recorded. A student from the community college is selected at random. The events A and B are defined as follows. A = event the student is at most 24 B = event the student is at least 40 Are the events A and B mutually exclusive
yes
Use the following information to answer the question. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric. In 2007, popular actor and singer Justin Timberlake was 26-years-old. What is Justin Timberlake's age in 2007 if it is standardized? Would it be unusual for a 26-year-old actor to be in a top-grossing film of 2007? Assume the Empirical Rule applies and round to the nearest hundredth.
z = -1.05; It would not be unusual.
Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric. In 2010, popular actress Jennifer Aniston was 41-years-old. What is Jennifer Aniston's age if it is standardized? Would it be unusual for a 41-year-old actress to be in a top-grossing film of 2010? Assume the Empirical Rule applies and round to the nearest hundredth.
z = 1.80; It would not be unusual.
The mean price of a pound of ground beef in 75 cities in the Midwest is $2.11 and the standard deviation is $0.56. A histogram of the data shows that the distribution is symmetrical. A local Midwest grocer is selling a pound of ground beef for $3.25. What is this price in standard units? Assuming the Empirical Rule applies, would this price be unusual or not? Round to the nearest hundredth.
z = 2.04; This is unusually expensive ground beef.
The top nine scores on the organic chemistry midterm are as follows. 74, 39, 80, 57, 43, 69, 21, 34, 69
20.5
Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. If a regulation basketball is randomly selected, what is the probability that it will weigh between 19.5 and 22.5 ounces? Round to the nearest thousandth.
0.685
At a course in public speaking, the instructor always gives an opening speech that lasts between fifteen and eighteen minutes. The length of the speech can be modeled by a uniform distribution, that is, the speech is just as likely to last fifteen minutes as it is to last eighteen minutes. The probability density curve is shown below. What is the probability that the speech will last sixteen minutes or more? What is the probability that the speech will last between eighteen and nineteen minutes?
0.75; 0.25
The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 5.0 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 3.5 and 6.0 minutes to find a parking spot in the library lot.
0.7745
Determine whether the variable would best be modeled as continuous or discrete: The number of cups dispensed from a beverage vending machine during a 24-hour period.
discrete
Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and two of your friends each draws a chip (with replacement), what is the probability that at least one of your group of three will win the valuable prize? Round to the nearest thousandth.
0.784
Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. If a regulation basketball is randomly selected, what is the probability that it will weigh between 20.5 and 23.5 ounces? Round to the nearest thousandth.
0.866
Suppose that a recent poll of American households about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually exclusive. What is the probability that at least two of the three randomly selected households own either a cat or a dog? (Round to the nearest hundredth)
0.89
A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 335 seconds to run the mile.
0.9893
A pollotarian is a person who eats poultry but no red meat. A wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of about 200,000. On average, what proportion of the guests would be expected to be pollotarian, give or take how many? Round to the nearest whole person.
11 people, give or take 3 people
There are four colors in a bag containing 500 plastic chips. It is known that 28% of the chips are green. On average, how many chips from a random sample of 50 (with replacement) would be expected to be green?
14
The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed. What is the travel time to work that separates the bottom 2.5% of people with the median or 50%? Round to the nearest tenth of a minute.
8 to 17 minutes
Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. Roughly what percentage of regulation basketballs weigh less than 20.7 ounces? Round to the nearest tenth of a percent.
9.7% of the basketballs will weigh less than 20.7 ounces.
Decide whether the experiment is a binomial experiment. If it is not, explain why. In a game you spin a wheel that has 11 different letters 450 times. The random variable represents the selected letter on each spin of the wheel.
Not a binomial experiment. There are more than two outcomes.
Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. Roughly what percentage of regulation basketballs weigh more than 23.1 ounces? Round to the nearest tenth of a percent.
Roughly 13.6% of the basketballs will weigh more than 23.1 ounces.
Assume 80% of adults with arthritis symptoms report relief with a specific medication. If a new medication is given to 10 new patients with symptoms, what is the probability that the medication effectively relieves their symptoms? Select the most accurate statement to investigate the assumptions for using a binomial distribution model.
The outcome is relief from symptoms, yes or no with relief as a yes. It is reasonable to assume that the replications are independent. The probability of success for each new patient is 0.8.
Suppose that the probability that a person between the ages of 19 and 24 checks their daily horoscope is 0.12. If 400 randomly selected people between the ages of 19 and 24 were asked "Do you check your daily horoscope?", would you be surprised if 63 or more said yes to this question? Why?
Yes, 63 would be an unusually small number of people given the known probability of 0.12.
There are four colors in a bag containing 600 plastic chips. It is known that 34% of the chips are yellow. On average, how many chips from a random sample of 30 (with replacement) would be expected to be yellow? Round to the nearest whole chip.
about 10
Determine whether the variable would best be modeled as continuous or discrete: The amount of time it takes students to get to school.
continuous
Determine whether the variable would best be modeled as continuous or discrete: The number of tails when flipping ten coins.
discrete
What generally happens to the sampling error as the sample size is decreased?
it gets larger
The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings. Management at the home improvement store randomly selected 170 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store.
number of items - discrete; total time - continuous
In a study of 900 adults, 45 out of the 325 men in the study said that they preferred to rent a movie on DVD rather than going out to a movie theater.What is the approximate percentage of men in this study who prefer to rent a movie on DVD?
13.8%
Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric. Between what two values would you expect to find about 95% of the lead actresses ages?
16.9 and 42.3 years
At one college, GPA's have a distribution that is unimodal and symmetric with a mean of 3.1 and a standard deviation of 0.6. What is the range of GPA's from one standard deviation below the mean to one standard deviation above the mean?
2.5 to 3.7
Use the following information to answer the question. The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours. If Anthony's z-score for his work hours was -1.3, how many hours did he work?
7.35 hours
Two Physics classes at Jefferson High School took the same quiz. Mr. Spears had 20 students in his class with a mean score of 80. Mrs. Guyton's class of 30 students had a mean score of 90. Overall, what was the mean score for all students on the quiz?
86
The National Center for Health Statistics has found that there is a 5.01% chance that an American citizen will die from an accident (unintentional injury). What is the probability that you will not die from an accident? (Round to the nearest hundredth of a percent)
94.99%
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 IQ score separating the bottom 40% from the top 60%.
96.2
The National Center for Health Statistics has found that there is a 0.41% chance that an American citizen will die from falling. What is the probability that you will not die from a fall? (Round to the nearest hundredth of a percent)
99.59%
A large state university conducted a survey among their students and received 300 responses. The survey asked the students to provide the following information:* Age* Year in School (Freshman, Sophomore, Junior, Senior)* Gender* GPA
A histogram because Age is a numerical variable.
What is the difference between a histogram and a relative frequency histogram?
A histogram uses counts to record how many observations are in a data set, and a relative histogram uses proportions.
Suppose the ages and heights of 100 randomly selected people were recorded. Which variable is the explanatory variable and which one is the response?
Age is the explanatory variable and height is the response because a person's age could explain his/her height.
In a survey, married couples were asked, "Do you have children?" The response was electronically recorded as a "1" for yes and a "0" for no. This is an example of .
Coded categorical data
A group of cancer patients is divided into two groups. One group is given a new drug to fight the side effects of chemotherapy and the other group is given a placebo. After three months they are asked to respond to a questionnaire about the frequency and severity of their side effects to see whether the new drug improved the overall negative side effects of chemotherapy.
Controlled experiment
A group of students is divided into two groups. One group listens to classical music while taking a math test and the other group takes the test in silence. The average test scores of the two groups are compared to see whether listening to music during a math test has an effect on scores.
Controlled experiment
Consider the following statement, "In a nationwide study, children on an all-organic diet are more alert in school than those not on an all-organic diet." Which of the following is a plausible confounding variable in this study?
School start times The quality of the non-organic diet Parents' social-economic status
A city planner says, "The typical commute to work for someone living in the city limits is less than the commute to work for someone living in the suburbs." What does this statement mean?
The center of the distribution of commute times for a city-dweller is less than the center of the distribution for those living in the suburbs.
Each day for twenty days a record store owner counts the number of customers who purchase an album by a certain artist. The data and a dotplot of the data are shown below: Data set: 1, 3, 4, 4, 5, 6, 7, 2, 3, 4, 4, 5, 6, 8, 2, 3, 4, 5, 6, 7, 9
The dotplot shows that this data has a roughly bell-shaped distribution.
The bar charts below depict the marital statuses of Americans, separated by gender. Which bar chart shows more variability in marital status? Why?
The female bar chart shows more variability because there are more observations in the different categories than there are for males.
Data was collected on hand grip strength of adults. The histogram below summarizes the data. Which statement is true about the distribution of the data shown in the graph?
The graph shows evidence that two different groups may have been combined into one collection.
Which of the following measurements is likely to have the most variation?
The individual weights in ounces of potatoes in a randomly selected crate of potatoes.
highway = 0.892 + 1.337 ∙ (City) Note that City is the estimated miles per gallon (mpg) a car gets while driving on city streets, and Highway is the estimated miles per gallon (mpg) a car gets while driving on highways. Interpret the intercept in the context of the data. State whether the value is meaningful
The intercept is 0.892. If a car gets 0 mpg in the city, it will get 0.892 mpg on the highway. The value is not meaningful because if a car is not moving, it cannot have a mpg value.
The bar charts below depict the veteran statuses of Americans, separated by gender. Which bar chart has more variability in veteran status? Why?
The male bar chart shows more variability because there are more observations in the different categories than there are for females.
The distributions of income in the United States is strongly skewed to the right. Which of the following is true?
The median income is smaller than the mean income.
The distribution of the number of "friends" all users of a popular social media site have is strongly skewed to the right. Which of the following is true?
The median number of friends is smaller than the mean.
A word cloud was created using the first chapter of John Green's The Fault in Our Stars. (Note that filler words such as "the," "a/an," and "and" were excluded from the plot.) According to the word cloud, what is the most common word in the first chapter of The Fault in Our Stars? Why?
The most common word is "augustus" because it is the largest in size.
A word cloud was created using the first chapter of John Green's The Fault in Our Stars. (Note that filler words such as "the," "a/an," and "and" were excluded from the plot.) What information is NOT explicitly portrayed in the word cloud?
The number of times each word occurs.
highway = 0.892 + 1.337 ∙ (City) Note that City is the estimated miles per gallon (mpg) a car gets while driving on city streets, and Highway is the estimated miles per gallon (mpg) a car gets while driving on highways. Interpret the slope in the context of the data.
The slope is 1.337. For every additional mpg a car gets in the city, its highway mpg is predicted to increase by 1.337.
Salary = 95000 + 1280 ∙ (Years) Note that Years is the number of years a professor has worked at a college, and Salary is the annual salary (in dollars) the professor earns. Interpret the slope in the context of the data.The slope is 1280.
The slope is 1280. For every additional year a professor works at a college, his/her salary is predicted to increase by $1,280.
Admission to a certain university is determined by an entry exam. The scores of this test are Normally distributed with a mean of 400 and a standard deviation of 60. Only students who score in the top 30% will be offered admission. Amy scores 425 on the test. Choose the most accurate statement.
The top 30% is defined with a score greater than or equal to 431.4 so she will not be admitted.
Use the following information to answer the question. The distribution of the number of hours of sleep people get per night is unimodal and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours. If Amanda slept 9.2 hours last night, would you consider this unusual?
Yes, 9.2 hours is more than 2 standard deviations above the mean.
A group of 500 patients who suffer from hypothyroidism, a condition in which your thyroid does not produce enough of certain hormones, were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication, and one that received a placebo pill. The results of the study are below. Was the new medication effective in treating hypothyroidism?
Yes, a higher percent of patients who took the medication had improved symptoms than the patients who took the placebo.
Use your intuition to decide whether the following two events are likely to be independent or associated. Event A: Drawing a club from a deck of cards. Event B: Drawing a card with a black symbol from a deck of cards.
a
Ticket sales per hour = -631.25 + 11.25(current temperature in °F) What is the predicted number of tickets sold per hour if the temperature is 79°F? Round to the nearest whole ticket.
about 258 tickets
The histogram below shows the distribution of pass rates on a swimming test taken by all children who completed a four week summer swim course at the local YMCA. What is the typical pass rate for the swim test?
about 75%
Use your intuition to decide whether the following two events are likely to be independent or associated. Event A: A randomly selected registered voter's political party affiliation is Republican Event B: A randomly selected registered voter opposes a new tax on fuel.
associated
Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 650 babies born at a local hospital. The random variable represents the number of boys.
binomial experiment
In a survey, high school graduates were asked "Did you play sports in high school?" The response was electronically recorded as a "1" for yes and a "0" for no. This is an example of .
coded categorical data
A group of students is divided into two groups. One group is a given a new chewable vitamin and the other group is given a placebo. After six months they are asked to fill out a questionnaire and given a health exam to see whether the new vitamin has health benefits that are better than a placebo.
controlled experiment
A homeowner notices that 8 out of 14 days the mail arrives before 3pm. She concludes that the probability that the mail will arrive before 3pm tomorrow is about 57%. Is this an example of a theoretical or empirical probability?
empirical
Is the following an example of theoretical probability or empirical probability? A fisherman notes that eight out of ten times that he uses a certain lure he catches a fish within an hour. He concludes that the probability that the lure will catch a fish on his fishing next trip is about 80%
empirical
A two-way table could be used for which of the following pairs of variables?
gender and favorite class
Classify the events as independent or not independent: Events A and B where the probability of event A occurring is 0.3, the probability of event B occurring is 0.8, and the probability of both event occurring is 0.24.
independent
Classify the events as independent or not independent: Events A and B where the probability of event A occurring is 0.6, the probability of event B occurring is 0.6, and the probability of both event occurring is 0.36.
independent
The annual profits of five large corporations in a certain area are given below. Which measure of central tendency should be used? $134,000, $142,000, $162,000, $132,000, $1,212,000
median
Classify the events as independent or not independent: Events A and B where the probability of event A occurring is 0.5, the probability of event B occurring is 0.7, and the probability of both event occurring is 0.34.
not independent
A doctor is interested in determining whether a certain medication increases the risk of high blood pressure. He reviews his patients' medical records and finds that a higher proportion of people who take the medication are suffering from high blood pressure.
observational study
Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 180 students and recorded how long it took each of them to find a parking spot. Which of the following types of graphs should NOT be used to display information concerning the students parking times?
pie chart
At one college, GPA's have a distribution that is unimodal and symmetric with a mean of 2.9 and a standard deviation of 0.4. Is a GPA of 3.8 more than one standard deviation above the mean?
yes