AP STATS SEMESTER 1 FINAL
The distribution of monthly rent for one-bedroom apartments in a city is approximately normal with mean $936 and standard deviation $61. A graduate student is looking for a one-bedroom apartment and wants to pay no more than $800 in monthly rent. Of the following, which is the best estimate of the percent of one-bedroom apartments in the city with a monthly rent of at most $800?
1.8%
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Rachel is at the 99th percentile in height for adult women, then her height in inches is closest to...
70
At a college, the scores on the chemistry final are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the calculus final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored an 81 on the chem final and 84 on the calculus final. Relative to the students in each respective class, which subject did the student do better in?
The student did equally well in each course
18 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 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 difficult). Which of the following correctly identifies why this is not a well designed experiment?
The study was not comparative-only one treatment was used
The histogram shown summarizes the responses of 100 people when asked, "What was the price of the last meal you purchased?" Based on the histogram, which of the following could be the interquartile range of the prices?
$5
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?
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?
0.140
At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?
0.17
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. 20% of all tropical storms will originate in the Atlantic Ocean, of which 20% will be classified as major 30% of all tropical storms will originate in the eastern Pacific Ocean, of which 15% will be classified as major 50% of all tropical storms will originate in the western Pacific Ocean, of which 25% will be classified as major 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?
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?
0.19
For flights from a particular airport in January, there is a 30% chance of a flight being delayed because of icy weather. If a flight is delayed because of icy weather, there is a 10% chance of it also being delayed because of a mechanical problem. If a flight is not delayed because of icy weather, there is a 5% chance that it will be delayed because of mechanical problems. If one flight is randomly selected from the airport in January, what is the probability that the flight selected will have at least one of the two types of delays?
0.335
In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 are silver. One car will be selected at random from the parking lot. If each car in the parking lot only has one color, which of the following cannot be the probability that the selected car will be green?
0.6
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?
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?
0.8704
An exponential relationship exists between the explanatory variable and the response variable in a set of data. The common logarithm of each value of the response variable is taken, and the least-squares regression line has an equation of log(ŷ) = 7.3 - 1.5x. Which of the following is the closest to the predicted value of the response variable for x = 4.8?
1.26
The caffeine content of 8-ounce cans of a certain cola drink is approximately normally distributed with mean 33 milligrams. A randomly selected 8-ounce can containing 35mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans have a caffeine content greater than 35mg?
12%
90% of the people who have a particular disease will have a positive result on any given diagnostic test. 90% of the people who do not have the disease will have a negative test result. If 5% of a certain population has the disease, what percent would test positive for the disease?
14%
The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds?
324 pounds
The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3-year-old boys. Duncan is 32 inches tall and is in the 32nd percentile of the distribution. Shane is 34 inches tall and is at the 62nd percentile of the distribution. Which of the following is closest to the mean of the height distribution?
33.21 in
Janelle collected data on the amount of time in minutes each person in a large sample of customers spent in a local store. The data also included recording the gender of each customer. These data were used to generate the boxplots shown. Which of the following statements is true?
Approximately half of the males spent at least as much time in the store as any female in the sample
Which of the following is the best description of a positive association between two variables?
As the value of one of the variables increases, the value of the other variable tends to increase
The buyer 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 numbers in that range. She then opens the six boxes with the corresponding numbers, examines all 25 controllers in each box, and determines the proportion of the 150 controllers that are defective. What type of sample is this?
Cluster random sample
At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables shows the distribution of responses?
Cone Cup Total Adults 50 20 70 Children 100 40 140 Total 150 60 210
Gina's doctor told her that the z-score for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.5. Which of the following is the best interpretation of this z-score?
Gina's systolic pressure is 1.5 standard deviations above the average systolic blood pressure of women her age
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?
Giving the survey to 30 students selected at random from each of the 8 dorms on campus
In a certain school district, students from grade 6 to 12 can participate in a school-sponsored community service activity. The following chart shows the relative frequency of students from each grade who participate in the community service activity.
Grade 12 had the least relative frequency of participating students
Which of the following statements about a least-squares regression analysis is true? A point with a large residual is an outlier A point with high leverage has a y-value that is not consistent with the other y-values in the set The removal of an influential point from a data set could change the value of the correlation coefficient
III only
For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long?
No, because 3 inches falls above the maximum value of the lengths in the sample
A researcher collected data on the age, in years, and the growth of sea turtles. The graph is a residual plot of the regression of growth versus age
No, because the graph displays a U-shaped pattern
Roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and median. Is Roger correct?
No, only the mean is likely to change greatly
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 is the population and sample of the study?
The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected
Grain moisture is a characteristic of grain that affects the price paid for the grain. A random sample of 28 loads of corn was evaluated for moisture as a percent of the total weight. A different random sample of 28 loads of soybeans was also evaluated for moisture. The data are displayed in the dotplots below. Based on the dotplots, which of the following is greater for the percent moisture of corn than for the percent moisture of soybeans?
The range
The following histogram summarizes the amount spent on plane tickets to travel home, in dollars, for a group of 30 college students. If the interval size decreased from $200 to $100, which of the following must remain the same on the new histogram?
The sum of the frequencies
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?
To decrease the variability in estimates of the mean commuting time
A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds' total length, in centimeters, and tail length, were recorded. The output shown in the table is from a least-squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59 cm and a tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner?
Underestimate, because the residual is positive
List the sample space and tell whether the outcomes are equally likely. A family has two children; record the number of girls.
{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.
{BB, BG, GB, GG}, equally likely
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?
105
A large store has a customer service department where customers can go to ask for help with store-related issues. According to the 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?
(4/4)(¾)(2/4)(¼)
For a random sample of 20 professional athletes, there is a strong, linear relationship between the number of hours they exercise per week and their resting heart rate. For the athletes in the sample, those who exercise more hours per week tend to have lower resting heart rates than those who exercise less. Which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and their resting heart rate?
-0.87
Opinion-polling organizations contact their respondents by sampling random telephone numbers. Assume that interviewers can now reach about 71% of US 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?
0.78
Shalise competed in a jigsaw competition where participants are timed on how long they take to complete puzzles of various sizes. Shalise completed a small puzzle in 75 minutes and a large puzzle in 140 minutes. For all participants, the distribution of completion time for the small puzzle was approximately normal with mean 60 minutes and standard deviation 15 minutes. The distribution of completion time for the large puzzle was approximately normal with mean 180 minutes and standard deviation 40 minutes. Approximately what percentage of the participants had finishing times greater than Shalise's for each puzzle?
16% on the small puzzle and 84% on the large puzzle
At a certain store, the distribution of weights of cartons of eggs is approximately normal with mean 26 ounces. Based on the distribution, which of the following intervals will contain the greatest proportion of cartons of large eggs at the store?
22 oz to 28 oz
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. The students were classified by their age. The following table summarizes the responses of the students by age-group. One student from the school will be selected at random. What is the probability that the student responded JOY given that the selected student is in the age-group 6 to 8 years old?
28/106
For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season?
350 yards
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...
50%
The histogram below displays the frequencies of waiting times, in minutes, for 175 patients at a dentist's office. Which of the following could be the median of the waiting times, in minutes?
7.25
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?
90
Dairy farmers are aware there is often a linear relationship between the age of a dairy cow and the amount of milk produced. The least-squares regression line produced from a random sample is Milk= 40.8 - 1.1 (Age). Based on the model, what is the difference in predicted amounts of milk produced between a cow of 5 years and a cow of 10 years?
A cow of 5 years is predicted to produce 5.5 more gallons per week
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?
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... The probability of being awarded the first job (Event A) is 0.75 The probability of being awarded the second job (Event B) is 0.5 The probability of being awarded both jobs (Event A and B) is 0.375 If the owner's beliefs are correct which of the following statements must be true concerning event A and B?
Event A and B are not mutually exclusive and are independent
A field researcher who studies lions conjectured that the more time a cub spends playing, the sooner the cub will begin to hunt. Observational data were collected from 20 lion cubs. The researcher recorded how long they spent playing and the age when they began hunting. Because male and female lions have different hunting behaviors, the researcher recorded the data for males and females separately. The two scatterplots show the data for the 10 female lions and the 10 male lions. Based on the scatterplots, for which gender does there appear to be evidence that the more time a lion cub spends playing, the sooner the cub is likely to begin hunting?
Female cubs only
A store owner reports that the probability that a customer who purchases a lawn mower will also purchase an extended warranty is .68. What is the best interpretation of the probability .68?
For all customers who purchase a lean mower, 68% will also purchase an extended warranty
A local television news 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?
I, II, and III
Researchers wanted to investigate whether babies have a sense of right and wrong. They showed each of 60 babies a puppet show in which the 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.
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 a survey is 0.4. 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?
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 the 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?
No, because P (B ⋂ S) = 5/78
Events D and E are independent, with P(D) = 0.6 and the P(D and E) = 0.18. Which of the following is true?
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, and high pH, to 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?
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?
Rooting for the away team and rooting for the home team
At a large airport, data were recorded for one month on how many baggage items were unloaded from each flight upon arrival as well as the time required to deliver all the baggage items on the flight to the baggage claim area. A scatterplot of the two variables indicated a strong, positive linear association between the variables. Which of the following statements is a correct interpretation of the word "strong" in the description of the association?
The actual time required to deliver all the items to the baggage claim area based on the number of items unloaded will be very close to the time predicted by a least-squares model.
One way to measure the duration of subterranean disturbances such as earthquakes and mining is to calculate the root-mean-square time. The following histograms summarize the distributions of the root-mean-square times for the sources of disturbances. Based on the histograms, which of the following correctly compares the two distributions?
The range of the earthquake disturbances is less than the median of the mining disturbances
A scatterplot of student heights, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true?
The slope of the least squares regression line increases and the correlation coefficient increases.
As part of a science experiment, a student recorded 10 measurements of the temperature of a liquid. One of the measurements was an outlier when compared to the other 9 measurements. Which of the following must be true about the 9 measurements, excluding the outlier, when compared with the 10 measurements?
The standard deviation of the 9 measurements is less than the standard deviation of the 10
A new restaurant is interested in determining the best time-temperature combination for roasting a 5-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 5 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?
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 14-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 statistically significant. Which of the following can be concluded from this study?
There is an association between cell phone use and accidents, but not necessarily a causal relationship
A tennis ball was thrown in the air. The height of the ball from the ground was recorded every millisecond from the time the ball was thrown until it reached the height from which it was thrown. The correlation between the time and the height was computed to be 0. What does this correlation suggest about the relationship between the time and height?
There is no linear relationship between time and height
In a large set of data that are approximately normally distributed, r is the value of the data set that has a z-score of -1.00 s is the value of the first quartile, and t is the value of the 20th percentile Which of the following is the correct order from the least to greatest for the values of r, s, and t?
r, t, s