AP Stats Midterm

In a certain school, 17 percent of the students are enrolled in a psychology course, 28 percent are enrolled in a foreign language course, and 32 percent are enrolled in either a psychology course or a foreign language course or both. What is the probability that a student chosen at random from this school will be enrolled in both a foreign language course and a psychology course? A. 0.05 B. 0.13 C. 0.20 D. 0.32 E. 0.45

0.13

The sale bin in a clothing store contains an assortment of t-shirts in different sizes. There are 9 small, 7 medium, and 4 large shirts. Alan is looking for a large shirt. He starts grabbing shirts one at a time and checking the size. After he checks each shirt, he leaves it outside the bin. What is the probability that the first large shirt he finds is the third one he checks? A. 0.004 B. 0.008 C. 0.120 D. 0.128 E. 0.140

0.140

A tropical storm is classified as major if it has sustained winds greater than 110 miles per hour. Based on data from the past two decades, a meteorologist estimated the following percentages about future storms. Based on the meteorologist's estimates, approximately what is the probability that a future tropical storm will originate in the Pacific Ocean and be classified as major? A. 0.045 B. 0.125 C. 0.170 D. 0.400 E. 0.960

0.170

At a California college, 22% of students speak Spanish, 5% speak French, and 3% speak both languages. What is the probability that a student chosen at random from the college speaks Spanish but not French? A. 0.02 B. 0.17 C. 0.19 D. 0.20 E. 0.24

0.19

For flights from a particular airport in January, there is a 30 percent chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem. If one flight is selected at random from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays? A.0.065 B. 0.335 C. 0.350 D. 0.450 E. 0.665

0.335

In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. One car will be selected at random from the parking lot. If each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green? A. 0 B. 0.1 C. 0.2 D. 0.5 E. 0.6

0.6

Opinion-polling organizations contact their respondents by sampling random telephone numbers. Assume that interviewers can now reach about 71% of U.S. households, while the percentage of those contacted who agree to cooperate with the survey is 31%. Each household, it can be safely assumed, is independent of the others. What is the probability of failing to contact a household or of contacting the household but not getting them to agree to the interview A. 0.20 B. 0.50 C. 0.51 D. 0.78 E. 0.80

0.78

At a sporting event, cheerleaders will throw 50 bundled T-shirts into the crowd. The T-shirt sizes consist of 10 small, 15 medium, and the remainder either large or extra large. Suppose Ana catches a T-shirt. What is the probability that she will catch a T-shirt that is not a size small? A. 0.10 B. 0.20 C. 0.50 D. 0.67 E. 0.80

0.80

A police officer is using a radar device to check motorists' speeds. Prior to beginning the speed check, the officer estimates that 40 percent of motorists will be driving more than 5 miles per hour over the speed limit. Assuming that the police officer's estimate is correct, what is the probability that among 4 randomly selected motorists, the officer will find at least 1 motorist driving more than 5 miles per hour over the speed limit? A. 0.0256 B. 0.1296 C. 0.3456 D. 0.8704 E. 0.9744

0.8704

A local television new station includes a viewer survey question about a current issue at the beginning of every evening news broadcast. Viewers are invited to use social media to respond to the question. The results of the survey are shared with the audience at the end of each broadcast. In relation to the opinions of the population of the region, which of the following is a possible reason why the results of such surveys could be biased? 1. Viewers with strong opinions about the current issue are more likely to respond than are viewers without strong opinions 2. The opinions of viewers of one television station are not necessarily representative of the population of a region 3. Viewers with access to social media are not necessarily representative of the population of a region A. 1 only B. 2 only C. 3 only D. 2 and 3 only E. 1,2, and 3

1, 2, and 3

A large store has a customer service department where customers can go to ask for help with store-related issues. According to store records, approximately ¼ of all customers who go to the service department ask for help finding an item. Assume the reason each customer goes to the service department is independent from customer to customer. Based on the approximation, what is the probability that at least 1 of the next 4 customers who go to the service department will ask for help finding an item? A. 4(1/4) B. 1- (1/4)^4 C. 1- (3/4)^4 D. 4 (1/4)^1 (3/4)^4 E. (4/4)(3/4)(2/4)(1/4)

1- (3/4)^4

A friend of yours plans to toss a fair coin 200 times. You watch the first 20 tosses and are surprised that she got 15 heads. But then you get bored and leave. How many heads do you expect her to have when she has finished all 200 tosses? A. 100 B. 105 C. 110 D. 115 E. 150

105

Ninety percent of the people who have a particular disease will have a positive result on a given diagnostic test. Ninety percent of the people who do not have the disease will have a negative result on this test. If 5 percent of a certain population has the disease, what percent of that population would test positive for the disease? A. 4.5% B. 5% C. 10% D. 14% E. 90%

14%

Students at a local elementary school were shown a painting and asked which emotion—joy, happiness, love, or anger—they felt by looking at the painting. What is the probability that the student responded joy given that the selected student is in the age group 6 to 8 years old A. 89/332 B. 28/332 C. 28/106 D. 106/332 E. 28/89

28/106

A fair coin has come up "heads" 10 times in a row. The probability that the coin will come up heads on the next flip is A. 50% B. 100% C. greater than 50% D. less than 50% E. it cannot be determined

50%

Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. Of the 80 male students who were surveyed, 60 had brown eyes. If eye color and gender are independent, how many female students surveyed would be expected to have brown eyes? A. 5 B. 20 C. 30 D. 90 E. 100

90

Measurements of water quality were taken from a river downstream from an abandoned chemical dumpsite. Concentrations of a certain chemical were obtained from 9 measurements taken at the surface of the water, 9 measurements taken at mid-depth of the water, and 9 measurements taken at the bottom of the water. What type of study was conducted, and what is the response variable of the study? A. An experiment was conducted, and the response variable is the concentration of the chemical B. An experiment was conducted, and the response variable is the depth of the water C. A census was conducted, and the response variable is the depth of the water D. An observational study was conducted, and the response variable is the concentration of the chemical E. An observational study was conducted, and the response variable is the depth of the water

An observational study was conducted, and the response variable is the concentration of the chemical

The SC electric company has bid on two electrical wiring jobs. The owner of the company believes that 1. The probability of being awarded the first job is 0.75; 2. The probability of being awarded the second job is 0.5; 3. The probability of being awarded both jobs is 0.375. If the owner's beliefs are correct, which of the following statements must be true concerning event A and event B? A. Event A and B are mutually exclusive and independent B. Event A and B are mutually exclusive and are not independent C. Event A and Event B are not mutually exclusive and are independent D. Event A and Event B are not mutually exclusive and are not independent E. Event A and Event B are not mutually exclusive, and independence cannot be determined with the information given

Event A and event B are not mutually exclusive and are independent

A store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is 0.68. Which of the following is the best interpretation of the probability 0.68 ? A. For all customers who purchase a lawn mower, 68% will also purchase an extended warranty B. For all customers of the store, 68% will purchase a lawn mower C. For all customers who purchase an extended warranty, 68% will use the warranty D. From the next 25 customers, 17 will purchase an extended warranty E. From the next 25 customers, 17 will purchase a lawn mower

For all customers who purchase a lawnmower, 68% will also purchase an extended warranty

Which of the following does not describe a sampling method that has a potential source of voluntary response bias for the administration of a survey about college athletics at a university? A. Giving the survey to 30 students selected at random from each of the eight dorms on campus B. Giving the survey to the first 50 students who call the university radio station after the broadcaster announces the survey on air C. Giving the survey to any student who stops at a table set up in the student union after the survey is advertised D. Giving the survey to all students who respond to an advertisement in the student newspaper E. Giving the survey to physical education majors who receive extra credit for completing the survey

Giving the survey to 30 students selected at random from each of the eight dorms on campus

Researchers wanted to investigate whether babies have a sense of right and wrong. They showed each of 60 babies a puppet show in which a red puppet was trying to open a heavy box lid. A second puppet, called the helper, would try to help the red puppet open the box, while a third puppet, called the hinderer, would try to slam the box lid down. After watching the show, each baby was presented with a tray containing the helper puppet and the hinderer puppet, and the researchers recorded which puppet the baby reached for. The researchers wanted to determine whether the babies would reach for the helper puppet more than the hinderer puppet. As part of the show, a green puppet and a yellow puppet served as the helper and hinderer. For each baby a coin was tossed to determine which color would serve which role. Which of the following is the most important reason for the random assignment of color to role in the study? A. Slamming the lid might cause wear on the hinderer puppet after 60 shows. The random assignment of color to role permits more even wear between the helper and the hinderer B. The puppeteer might grow tired of doing the same show with the same puppet colors. The random assignment of color to role keeps the show fresh for each performance C. IF the same role is played by the same color puppet, the babies might show a preference for the color instead of a preference for the role D. The random assignment of color to role allows the researchers to determine if one color is better than another in teaching babies right from wrong E. Boys and girls might prefer different colors. The random assignment of color to role ensures that the show is equally accessible to boys and girls

If the same role is played by the same color puppet, the babies might show a preference for the color instead of a preference for the role

The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. Is Avery interpreting the probability correctly? A. Yes, because 2 out of 5 is equal to 40% B. Yes, because participants in the survey are selected at random C. No, because there could be voluntary response bias D. No, because only 40% of all people will visit the site E. No, because 0.40 represents probability in the long run over many visits to the site.

No, because 0.40 represents probability in the long run over many visits to the site.

A high school science teacher has 78 students. Of those students, 35 are in band and 32 are on a sports team. There are 16 students who are not in the band or on a sports team. One student from the 78 students will be selected at random. Let event B represent the event of selecting a student in the band, and let event S represent the event of selecting a student on a sports team. Are B and S mutually exclusive events A. No, because P(B n S)=5/78 B. No, because P(B n S)= 48/78 C. No, because P(B n S)= 62/78 D. Yes, because P(B n S)=5/78 E. Yes, because P(B n S)= 62/78

No, because P (B n S)= 5/78

Events D and E are independent, with P(D) = 0.6 and P(D and E)=0.18. Which of the following is true? A. P(E)= 0.12 B. P(E)= 0.4 C. P(D or E)= 0.28 D. P(D or E)= 0.72 E. P(D or E)= 0.9

P(D or E)= 0.72

Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, t the water in the tanks that hold the jellyfish. Which of the following is the best reason for the random assignment of a treatment level to an experimental unit? A. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects B. Randomization will make up for improper experimental design, data collections, and analysis C. Randomization makes the analysis easier since the data can be entered into the computer in any order D. Randomization is required by statistical consultants before they will analyze the experiment E. Randomization means that the experiment would not need to be replicated

Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects

The table shows data that were collected from people who attended a certain high school basketball game and indicates the team each person rooted for and whether each of these people purchased food during the game. A person who attended the game will be selected at random. Which of the following correctly interprets mutually exclusive events represented by the table? A. Rooting for the home team and rooting for the away team B. Rooting for the home team and purchasing food during the game C. Rooting for the away team and purchasing food during the game D. Rooting for the home team and not purchasing food during the game E. Not rooting for the home team and not purchasing food during the game

Rooting for the home team and rooting for the away team

as part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis. What are the population and the sample of the study? A. The population is the 770 students who were selected, and the sample is the 493 students who indicate that they use the exercise facilities on a regular basis B. The population is the 770 students who were selected, and the sample is whether each student in the survey uses the exercise facility on a regular basis C. The population is the 34,000 students who attend the university, and the sample is whether each student in the survey is male or female D. The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected E. The population is the 34,000 students who attend the university, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis

The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected

Eighteen individuals who use a particular form of social media were assigned a new user interface to use when logging in to their accounts. After using the new user interface for a week, each individual was asked to rate how easy or hard the new user interface was to use on a scale from 1 (extremely easy) to 9 (extremely hard). Which of the following correctly identifies why this is not a well designed experiment? A. There was a lack of control because not all individuals in the study used login passwords of the same length B. The individuals may not have been randomly selected C. There was not enough replication because the individuals used the new user interface for only one week D. There was a lack of control because not all individuals in the study use social media E. The study was not comparative- only one treatment was used

The study was not comparative- only one treatment was used

A new restaurant is interested in determining the best time-temperature combination for roasting a five-pound cut of lamb. The times to be tested are 45 minutes, 60 minutes, and 90 minutes at temperatures of 350 degrees Fahrenheit and 425 degrees Fahrenheit for each time, with the exception of the 90 minute - 425 degree combination. That combination is being eliminated because it will overcook the lamb, which leaves five combinations remaining. From 10 identical cuts of lamb, 2 are randomly selected to roast using each of the time-temperature combinations in the same oven. The quality of the finished product is evaluated for each roast. Which of the following is true? A. The explanatory variable is the quality of the finished lamb B. The response variable is the roasting temperature for the lamb C. If the experiment is repeated, identical results will be expected D. There should be a control group E. The two cuts that are being roasted for each time-temperature combination are an example of replication

The two cuts that are being roasted for each time-temperature combination are an example of replication

A recent study examined 699 car accidents in Toronto over a fourteen-month period. Records of phone-service providers were used to determine whether the driver was using a cell phone during or immediately before the accident. Overall, the researchers found that drivers using cell phones were 4.3 times as likely to have an accident as drivers who were not using cell phones. The result was significantly significant. Which of the following can be concluded from this study? A. Cell phone use increases the likelihood of a car accident B. There is an association between cell phone use and accidents, but not necessarily a causal relationship C. There is a correlation between cell phone use and accidents, but not necessarily an association D. The association between cell phone use and accidents is negative E. Cell phone use causes more accidents in Canada, but not necessarily in the United States

There is an association between cell phone use and accidents, but not necessarily a causal relationship

A regional transportation authority is interested in estimating the mean number of minutes working adults in the region spend commuting to work on a typical day. A random sample of working adults will be selected from each of three strata: urban, suburban, and rural. Selected individuals will be asked the number of minutes they spend commuting to work on a typical day. Why is stratification used in this situation? A. To remove bias when estimating the proportion of working adults living in urban, suburban, and rural areas B. To remove bias when estimating the mean commuting time C. To reduce bias when estimating the mean commuting time D. To decrease the variability in estimates of the proportion of working adults living in urban, suburban, and rural areas E. To decrease the variability in estimates of the mean commuting time

To decrease the variability in estimates of the mean commuting time

The buyers for an electronics store wants to estimate the proportion of defective wireless game controllers in a shipment of 5,000 controllers from the store's primary supplier. The shipment consists of 200 boxes each containing 25 controllers. The buyer numbers the boxes from 1 to 200 and randomly selects six boxes in that range. She then opens the six boxes with the corresponding numbers, examines all 25 controllers in each of these boxes, and determines the proportion of the 150 controllers that are defective. What type of sample is this? A. biased random sample B. nonrandom sample C. simple random sample D. stratified random sample E. cluster random sample

cluster random sample

List the sample space and tell whether the outcomes are equally likely. A family has two children; record the number of girls. A. {0,1}, equally likely B. {1, 2}, equally likely C. {1,2} not equally likely D. {0,1,2}, equally likely E. {0,1,2}, not equally likely

{0,1,2}, not equally likely

List the sample space and tell whether the outcomes are equally likely. A family has two children; record the genders in order of birth. A. {BB, BG, GB, GG}, not equally likely B. {BB, BG, GB, GG}, equally likely C. {B, G}, equally likely D. {BB, BG, GG}, not equally likely E. {BB, BG, GG}, equally likely

{BB, BG, GB, GG}, equally likely